Definition of an inner and outer product of two column vectors.
Take my Coursera course at
https://www.coursera.org/learn/matrix-algebra-engineers
Download lecture notes from
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

Views: 1597
Jeffrey Chasnov

This video shows the difference between inner product and outer product of two vectors and shows how to calculate them using a TI-83 calculator.

Views: 18362
Mr13things

Defining and understanding what it means to take the product of a matrix and a vector
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/introduction-to-the-null-space-of-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices-reduced-row-echelon-form-3?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 239982
Khan Academy

Views: 1566
118yt118

Visual interpretation of the cross product and the dot product of two vectors.
My Patreon page: https://www.patreon.com/EugeneK

Views: 389143
Physics Videos by Eugene Khutoryansky

This covers the main geometric intuition behind the 2d and 3d cross products.
*Note, in all the computations here, I list the coordinates of the vectors as columns of a matrix, but many textbooks put them in the rows of a matrix instead. It makes no difference for the result, since the determinant is unchanged after a transpose, but given how I've framed most of this series I think it is more intuitive to go with a column-centric approach.
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Views: 375028
3Blue1Brown

Understanding the differences between the dot and cross products. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/electric-motors/v/calculating-dot-and-cross-products-with-unit-vector-notation?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Missed the previous lesson? https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/electric-motors/v/the-dot-product?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Physics channel: https://www.youtube.com/channel/UC0oGarQW2lE5PxhGoQAKV7Q?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 424149
Khan Academy

This physics video tutorial explains how to find the cross product of two vectors using matrices and determinants and how to confirm your answer using the dot product formula. This video contains plenty of examples and practice problems using the components i j k.

Views: 51978
The Organic Chemistry Tutor

This lesson discusses the notations involved with the dot product, and the notation that is involved with the inner product. We will go more in depth in the actual book.

Views: 6916
JJtheTutor

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 47563
MathTheBeautiful

MIT 8.05 Quantum Physics II, Fall 2013
View the complete course: http://ocw.mit.edu/8-05F13
Instructor: Barton Zwiebach
In this lecture, the professor continued to talk about the tensor product and also talked about entangled states, Bell basis states, quantum teleportation, etc.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 9652
MIT OpenCourseWare

Definition of a 2nd order tensor, examples zero tensor, identity tensor, and tensor outer product with two additional examples of tensor outer product tensors.

Views: 5297
Sanjay Govindjee

Dot and Cross Product Comparison/Intuition
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/vector-triple-product-expansion-very-optional?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proof-relationship-between-cross-product-and-sin-of-angle?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 242640
Khan Academy

The Exterior Algebra of a linear space (vector space) is also known as the Grassmann Algebra, and sometimes as the Multi-vector Algebra of a vector space. Any n dimensional linear space (vector space) can be associated with a collection of related spaces that are obtained by means of the wedge product between vectors. Here we define the wedge product abstractly by three rules. Left and right associative and the null product that generates the zero vector of the 2nd exterior power space. The exterior product space consists of n+1 subspaces each having dimension C(n,p) where C is the binomial coefficient. Compound products of basis vectors of the base linear space become the basis vectors of the exterior power spaces. The direct sum of all exterior power spaces is a linear space of dimension 2^n and has the property of being closed under the wedge product. We introduce the discrete topological space of basis vectors and construct the exterior algebra from the discrete topology tau-n of a basis set of Vn.

Views: 13189
Mathview

Recorded: 2014-12-19
Playlist: https://www.youtube.com/watch?v=leb1hMPC274&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl&index=4
A discussion of the use of an outer product.
0:30 The difference between an outer product and inner (dot) product depends on whether you put the vertical matrix followed by the horizontal matrix, or vice versa.
1:50 The outer product, sometimes denoted $\vec A \otimes \vec B$, ends up being a 3x3 matrix (a rank 2 tensor).
2:35 Sarrus' rule for doing a cross product. (which I'm not terribly good at, and it takes me a long time.)
5:45 A physical interpretation of the cross product. Magnitude according to the area of a parallelogram. Direction according to the right-hand-rule.
7:00 Magnitude = A*B*sin(\theta)
8:10 Using the outer product and Levi-Cevita to help us do the cross product.
9:10 I need to make up a new notation for a sum of the products.
10:00 The dot product of two vectors is the TRACe of the outer product of the two vectors.
10:45 I make a surprising number of mistakes in taking this outer product.
11:30 Finally it's correct.
12:00 Now I'm trying to get the outer product to do the work of a cross product.
13:55 Re-writing this outer-product method of getting the cross product.
15:10 Using the Levi Cevita symbol to do the cross-product.
16:00 Fixing my equation to show that it's not really a matrix multiplication.
16:30 Enshrining these formulas into LaTeX.
17:30 Equation 4 has this outer-product term... So I thought it was important before figuring how to do a transformation of an outer product, it might be nice to figure out what the outer product was for in the first place.
19:15 Oh, this thing $\delta_{mn}$ is called a Kroeniker Delta function... Not the Dirac Delta function

Views: 1868
Jonathan Doolin

This video explains what is meant by the Kronecker Product of two matrices, and discusses some of this operation's uses in econometrics.
Check out http://oxbridge-tutor.co.uk/graduate-econometrics-course/ for course materials, and information regarding updates on each of the courses. Check out https://ben-lambert.com/econometrics-course-problem-sets-and-data/ for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: https://ben-lambert.com/bayesian/ Accompanying this series, there will be a book: https://www.amazon.co.uk/gp/product/1473916364/ref=pe_3140701_247401851_em_1p_0_ti

Views: 20745
Ben Lambert

This video demonstrates the GeoGebra worksheet, "Inner and Outer Products of Vectors Inscribed in a Circle"
http://tube.geogebra.org/material/show/id/1015919
This resource is part of a series that I am preparing in support of Professor David Hestenes's goal of using Geometric Algebra(GA) to integrate high-school algebra,geometry, trigonometry,and physics into a coherent curriculum.
Resources prepared by Professor Hestenens and Robert Rowley
http://geocalc.clas.asu.edu/GA_Primer/GA_Primer/
http://geocalc.clas.asu.edu/GA_Primer/GA_Primer/introduction-to-geometric/high-school-geometry-with/index.html
Wiki for collaborative development of pre-university materials on GA
http://preuniversitygeometricalgebra.wikispaces.com/
LinkedIn group for the same purpose:
Pre-University Geometric Algebra
https://www.linkedin.com/groups?home=&gid=8278281
See also, in this series,
Dot Product: Geometric Significance and GeoGebra Coding
http://tube.geogebra.org/material/show/id/949399

Views: 431
JimSmithInChiapas

Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation.
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Views: 521954
3Blue1Brown

See also the document "Rotations of Vectors via Geometric Algebra: Explanation, and Usage in Solving Classic Geometric "Construction" Problems (Version of 11 February 2016)", which is available via the links
http://www.slideshare.net/JamesSmith245/rotations-of-vectors-via-geometric-algebra-explanation-and-usage-in-solving-classic-geometric-construction-problems-version-of-11-february-2016
https://www.dropbox.com/s/m14da332flq76oy/Rotations%20Print%20version%2011%20Feb%202016.pdf?dl=0
https://drive.google.com/file/d/0B2C4TqxB32RRdE5KejhQTzMtN3M/view?usp=sharing
This video presents an unconventional development -- which might be helpful -- of Geometric Algebra's outer product. The video shows one section of an interactive GeoGebra worksheet that reviews the basics of vectors in depth, then uses the dot product to solve the problem
"Given two known vectors 'a' and 'b', and the values of their dot products with an unknown third vector, 'x' that is coplanar with 'a' and 'b', find 'x."
The interactive worksheet can be used online or downloaded at
http://tube.geogebra.org/m/1481375.
A video based upon that worksheet is
"Geometric (Clifford) Algebra: Find an unknown vector from two of its dot products "
https://www.youtube.com/watch?v=2cqDVtHcCoE
That worksheet builds upon a previous one on the geometric significance of the dot product, and how to code that product in GeoGebra. That worksheet can be used or downloaded at
http://tube.geogebra.org/material/show/id/949399,
and viewed at
https://www.youtube.com/watch?v=eV5jQcuRQmU.

Views: 655
JimSmithInChiapas

Leave a tip for good service: https://paypal.me/jjthetutor
Student Solution Manuals: https://amzn.to/2WZrFnD
More help via http://jjthetutor.com
Download my eBooks via http://payhip.com/jjthetutor,
paperback via http://amazon.com/author/jjthetutor.

Views: 16666
JJtheTutor

Linear Algebra 101 – 1.7: Products of Two Vectors
What are the possible products of two vectors in 2D space?
©WCCS
Walnut Creek, CA 94596 Of The U.S.A.
5 Various Products of Two Vectors on 2D space are covered in this presentation:
• Inner Product, Scalar Product, Dot Product
• Outer Product, Tensor Product
• Cross Product, Vector Product
• Determinant Product
• Complex Number Product

Views: 159
Ray FunMath

Learn the theory of Vector (Cross or Outer) product between two vectors. This tutorial explains the right hand rule for determining the direction of resultant vector obtained at the end of vector product. This tutorial also explains properties of vector product.
Links of my other videos.
Basic maths revision in gujarati.
https://www.youtube.com/watch?v=Pfufinr3qJI
Logarithm theory in gujarati.
https://www.youtube.com/watch?v=YeAbHAWj9Jo
Logarithm solved examples in gujarati.
https://www.youtube.com/watch?v=_V8PqxsnguU
Determinants of second order theory in gujarati.
https://youtu.be/vJKpXfRvJSo
Determinants of second order solved examples in gujarati.
https://youtu.be/-yQoPDgTadI
Determinants of third order theory in gujarati.
https://youtu.be/94Pmvv3jerQ
Third order determinant minor and cofactor solved example in gujarati.
https://youtu.be/t-Xx1_ruJTY
Expansion of third order determinant theory in gujarati.
https://youtu.be/tdQRNW4g9YY
Expansion of third order determinant solved example in gujarati.
https://youtu.be/sHLUmUA31Nk
Sarrus method for expansion theory in gujarati.
https://youtu.be/ChimYbo-Rcs
Sarrus method for expansion solved examples in gujarati.
https://youtu.be/uDScdGI3LYs
Properties of determinants in guajrati.
https://youtu.be/Z4jXBrAYozc
Properties of determinats solved examples in gujarati.
https://youtu.be/U3KOmXGQ9SY
Matrices theory in gujarati.
https://youtu.be/0w_HU0c_w3I
Equality of matrices solved examples in gujarati.
https://youtu.be/WsCmeg-NEBs
Types of matrices theory in gujarati.
https://youtu.be/hBkW9Qr09Y0
Addition of matrices solved examples in gujarati.
https://youtu.be/A0FBl8TtneQ
Product of matrices theory in gujarati.
https://youtu.be/VR1IU365e9Y
Multiplication of matrices solved examples in gujarati.
https://youtu.be/DAdc2iQSQt4
Transpose and adjoint of a matrix theory in gujarati.
https://youtu.be/FVnG_YKyEew
Adjoint of a matrix solved examples in gujarati.
https://youtu.be/CosMn2IHtaI
Inverse of a matrix theory in gujarati.
https://youtu.be/6l4ZZwRDHzo
Inverse of a matrix solved examples in gujarati.
https://youtu.be/qAcL7mcd8AQ
Unique solution of system of linear equations in two variables theory in gujarati.
https://youtu.be/DUh9UqvSwbQ
Unique solution of system of linear equations in two variables solved examples in gujarati.
https://youtu.be/F2fe8jEWiGE
Unique solution of system of linear equations in three variables theory in gujarati.
https://youtu.be/Qj7SXAz_-mI
Unique solution of system of linear equations in three variables solved examples in gujarati.
https://youtu.be/5kwQQix20Us
Vector algebra theory in gujarati.
https://youtu.be/uvPN6TYoAKk
Vector algebra solved example in gujarati.
https://youtu.be/X3mSoQOHXsg
Scalar (Dot or Inner) product theory in gujarati.
https://youtu.be/2vUYjkn9W6E
Scalar Dot or Inner product solved examples in gujarati.
https://youtu.be/HMaywExDPYo
Vector (Cross or Outer) product theory in gujarati.
https://youtu.be/uMV4LtVUfSQ
Area theory in gujarati.
https://www.youtube.com/watch?v=qRKx7bDLk8A
Area solved examples in gujarati.
https://www.youtube.com/watch?v=i8y2jWv2LrE
Volume theory in gujarati.
https://www.youtube.com/watch?v=T8vEoPJZ5W8
Volume solved examples in gujarati.
https://www.youtube.com/watch?v=ZNjUFq_9wp0

Views: 45
JB's Mathematics

This video tutorial teaches how to do vector product of two given vectors. There are couple of solved examples explaining cross product. of two vectors.
Links of my other videos.
Basic maths revision in gujarati.
https://www.youtube.com/watch?v=Pfufinr3qJI
Logarithm theory in gujarati.
https://www.youtube.com/watch?v=YeAbHAWj9Jo
Logarithm solved examples in gujarati.
https://www.youtube.com/watch?v=_V8PqxsnguU
Determinants of second order theory in gujarati.
https://youtu.be/vJKpXfRvJSo
Determinants of second order solved examples in gujarati.
https://youtu.be/-yQoPDgTadI
Determinants of third order theory in gujarati.
https://youtu.be/94Pmvv3jerQ
Third order determinant minor and cofactor solved example in gujarati.
https://youtu.be/t-Xx1_ruJTY
Expansion of third order determinant theory in gujarati.
https://youtu.be/tdQRNW4g9YY
Expansion of third order determinant solved example in gujarati.
https://youtu.be/sHLUmUA31Nk
Sarrus method for expansion theory in gujarati.
https://youtu.be/ChimYbo-Rcs
Sarrus method for expansion solved examples in gujarati.
https://youtu.be/uDScdGI3LYs
Properties of determinants in guajrati.
https://youtu.be/Z4jXBrAYozc
Properties of determinats solved examples in gujarati.
https://youtu.be/U3KOmXGQ9SY
Matrices theory in gujarati.
https://youtu.be/0w_HU0c_w3I
Equality of matrices solved examples in gujarati.
https://youtu.be/WsCmeg-NEBs
Types of matrices theory in gujarati.
https://youtu.be/hBkW9Qr09Y0
Addition of matrices solved examples in gujarati.
https://youtu.be/A0FBl8TtneQ
Product of matrices theory in gujarati.
https://youtu.be/VR1IU365e9Y
Multiplication of matrices solved examples in gujarati.
https://youtu.be/DAdc2iQSQt4
Transpose and adjoint of a matrix theory in gujarati.
https://youtu.be/FVnG_YKyEew
Adjoint of a matrix solved examples in gujarati.
https://youtu.be/CosMn2IHtaI
Inverse of a matrix theory in gujarati.
https://youtu.be/6l4ZZwRDHzo
Inverse of a matrix solved examples in gujarati.
https://youtu.be/qAcL7mcd8AQ
Unique solution of system of linear equations in two variables theory in gujarati.
https://youtu.be/DUh9UqvSwbQ
Unique solution of system of linear equations in two variables solved examples in gujarati.
https://youtu.be/F2fe8jEWiGE
Unique solution of system of linear equations in three variables theory in gujarati.
https://youtu.be/Qj7SXAz_-mI
Unique solution of system of linear equations in three variables solved examples in gujarati.
https://youtu.be/5kwQQix20Us
Vector algebra theory in gujarati.
https://youtu.be/uvPN6TYoAKk
Vector algebra solved example in gujarati.
https://youtu.be/X3mSoQOHXsg
Scalar (Dot or Inner) product theory in gujarati.
https://youtu.be/2vUYjkn9W6E
Scalar Dot or Inner product solved examples in gujarati.
https://youtu.be/HMaywExDPYo
Vector (Cross or Outer) product theory in gujarati.
https://youtu.be/uMV4LtVUfSQ
Vector (Cross or Outer) product of solved examples in gujarati.
https://youtu.be/U692LUTRDDw
Area theory in gujarati.
https://www.youtube.com/watch?v=qRKx7bDLk8A
Area solved examples in gujarati.
https://www.youtube.com/watch?v=i8y2jWv2LrE
Volume theory in gujarati.
https://www.youtube.com/watch?v=T8vEoPJZ5W8
Volume solved examples in gujarati.
https://www.youtube.com/watch?v=ZNjUFq_9wp0

Views: 43
JB's Mathematics

Views: 123
Mark Homan

Part II of the preliminary vector stuff section of this series on Tensor Calculus. We go over transformations through rotation, space-time interval invariance, transformation coefficients as partial derivatives, vectors as Matrices (Bra-Ket Notation), outer products, completeness, calculating matrix elements, and change of basis.

Views: 4124
Andrew Dotson

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! In this video, I give the formula for the cross product of two vectors, discuss geometrically what the cross product is, and do an example of finding the cross product.
For more free math videos, visit http://PatrickJMT.com

Views: 730948
patrickJMT

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! For more FREE math videos, visit http://PatrickJMT.com !!
Vectors - The Dot Product. I show how to compute the dot product of two vectors, along with some useful theorems and results involving dot products. 3 complete examples are shown.

Views: 865935
patrickJMT

We can use indices to write matrix multiplication in a more compact way.

Views: 10871
PhysicsHelps

Outer Product from the EP 'The Monte Carlo Step'

Views: 2280
David Peek

Subject: Mathematics
Paper: Differential geometry
Module: Introduction of tensors: contravariant and covariant vectors (MAT)
Content Writer: Dr. Arindam Bhattacharya

Views: 18463
Vidya-mitra

Error: at around 13:25, on the last line, the input space should be V-tensor-(V*), not (V*)-tensor-V, although the two spaces are involve vector-covector pairs, the order is different, and so they are technically different spaces.
This one took a while to edit... kept noticing mistakes and having to go back and fix them. I'm sure there's at least

Views: 9262
eigenchris

What is a Tensor 5: Tensor Products
Errata: At 22:00 I write down "T_00 e^0 @ e^1" and the correct expression is "T_00 e^0 @ e^0"

Views: 30485
XylyXylyX

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 5153
MathTheBeautiful

Linear Algebra: We define the standard inner product on R^n and explain its basic properties. A cosine formula is given in terms of the inner product and lengths of two vectors.

Views: 24568
MathDoctorBob

There are a wide variety of different vector formalisms
currently utilized in engineering and physics. For example, Gibbs’ three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford’s multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.

Views: 12027
UniAdel

Interpretations of A.B in terms of dot products of rows of A with columns of B, A with columns of B, rows of A with B, row matrices of A with column matrices of B, sum of outer products of columns of A with corresponding rows of B. AX, X a vector, is the linear combination of columns of A with weights same as entries of vector X.

Views: 86
online math

Rejaul Makshud is an Author of Booster Series for JEE Main and Advanced Exams in Mcgraw Hill Publication (I) Pvt Ltd.
Cross product/Vector Product / Outer Product of two vectors, its meaning, its geometrical significance, its properties, its numerical problems which can be asked in IIT-JEE / ISC / CBSE .
RACE IIT ACADEMY is a premier coaching institute for the preparation of JEE (Main+Advanced), JEE (Main), Pre-Medical (AIPMT / AIIMS). The Institute is well regarded for the high quality entrance exams preparation and produces best results year after year.
At RACE IIT, we focus on building a strong foundation of knowledge and concepts in students for their success and provide an excellent platform for the preparation of competitive exams and board level education. The best academic support and personal care which we provide to the students helps them meet their career goals and objectives.
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Views: 61
Race IIT Academy

This video tutorial gives the practice of calculating the moment of a force about a point using cross product of two vectors.
Links of my other videos.
Basic maths revision in gujarati.
https://www.youtube.com/watch?v=Pfufinr3qJI
Logarithm theory in gujarati.
https://www.youtube.com/watch?v=YeAbHAWj9Jo
Logarithm solved examples in gujarati.
https://www.youtube.com/watch?v=_V8PqxsnguU
Determinants of second order theory in gujarati.
https://youtu.be/vJKpXfRvJSo
Determinants of second order solved examples in gujarati.
https://youtu.be/-yQoPDgTadI
Determinants of third order theory in gujarati.
https://youtu.be/94Pmvv3jerQ
Third order determinant minor and cofactor solved example in gujarati.
https://youtu.be/t-Xx1_ruJTY
Expansion of third order determinant theory in gujarati.
https://youtu.be/tdQRNW4g9YY
Expansion of third order determinant solved example in gujarati.
https://youtu.be/sHLUmUA31Nk
Sarrus method for expansion theory in gujarati.
https://youtu.be/ChimYbo-Rcs
Sarrus method for expansion solved examples in gujarati.
https://youtu.be/uDScdGI3LYs
Properties of determinants in guajrati.
https://youtu.be/Z4jXBrAYozc
Properties of determinats solved examples in gujarati.
https://youtu.be/U3KOmXGQ9SY
Matrices theory in gujarati.
https://youtu.be/0w_HU0c_w3I
Equality of matrices solved examples in gujarati.
https://youtu.be/WsCmeg-NEBs
Types of matrices theory in gujarati.
https://youtu.be/hBkW9Qr09Y0
Addition of matrices solved examples in gujarati.
https://youtu.be/A0FBl8TtneQ
Product of matrices theory in gujarati.
https://youtu.be/VR1IU365e9Y
Multiplication of matrices solved examples in gujarati.
https://youtu.be/DAdc2iQSQt4
Transpose and adjoint of a matrix theory in gujarati.
https://youtu.be/FVnG_YKyEew
Adjoint of a matrix solved examples in gujarati.
https://youtu.be/CosMn2IHtaI
Inverse of a matrix theory in gujarati.
https://youtu.be/6l4ZZwRDHzo
Inverse of a matrix solved examples in gujarati.
https://youtu.be/qAcL7mcd8AQ
Unique solution of system of linear equations in two variables theory in gujarati.
https://youtu.be/DUh9UqvSwbQ
Unique solution of system of linear equations in two variables solved examples in gujarati.
https://youtu.be/F2fe8jEWiGE
Unique solution of system of linear equations in three variables theory in gujarati.
https://youtu.be/Qj7SXAz_-mI
Unique solution of system of linear equations in three variables solved examples in gujarati.
https://youtu.be/5kwQQix20Us
Vector algebra theory in gujarati.
https://youtu.be/uvPN6TYoAKk
Vector algebra solved example in gujarati.
https://youtu.be/X3mSoQOHXsg
Scalar (Dot or Inner) product theory in gujarati.
https://youtu.be/2vUYjkn9W6E
Scalar Dot or Inner product solved examples in gujarati.
https://youtu.be/HMaywExDPYo
Vector (Cross or Outer) product theory in gujarati.
https://youtu.be/uMV4LtVUfSQ
Vector (Cross or Outer) product of solved examples in gujarati.
https://youtu.be/U692LUTRDDw
Applications of Vector product theroy in gujarati
https://youtu.be/yN87B41Lqhs
Applications of Vector product solved examples in gujarati
https://youtu.be/qRfD8FG1LA0
Moment of a force about a point theory in gujarati.
https://youtu.be/ggJDOB7778U
Moment of a force about a point solved examples in gujarati.
https://youtu.be/7L3FdaSwyJ0
Area theory in gujarati.
https://www.youtube.com/watch?v=qRKx7bDLk8A
Area solved examples in gujarati.
https://www.youtube.com/watch?v=i8y2jWv2LrE
Volume theory in gujarati.
https://www.youtube.com/watch?v=T8vEoPJZ5W8
Volume solved examples in gujarati.
https://www.youtube.com/watch?v=ZNjUFq_9wp0

Views: 38
JB's Mathematics

An introductory video on the Cross Product of two vectors and its application.

Views: 587
Cuong Ngo

An overview of the concepts from linear algebra that well be using in CompSci 369 Computational Science. Use links below to directly go to specific topics in the review.
0:00 Matrix definition
1:15 Matrix transpose
3:04 Matrix product
7:24 Vector definition
9:41 Dot product
12:53 Magnitude of a vector
14:36 Outer product
16:39 Product of a matrix and vector
19:33 Identity matrix
21:26 Matrix inverse
22:13 Invertible and singular matrices
22:55 Determinants
26:55 Properties of the determinant
28:46 Eigenvalues and eigenvectors
32:27 Example: finding eigenvalues
32:27 Example: finding eigenvectors
37:58 Orthogonal vectors
39:11 Mutually orthogonal sets
39:51 Normalised vectors
40:35 Orthonormal sets
41:06 Eigenvalues of a square symmetric matrix
42:09 Eigenvector representation of a matrix

Views: 303
David Welch

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 9298
MathTheBeautiful

Definition of an inner product and some examples

Views: 37599
Gilbert Eyabi