Math 060 Fall 2017 103017C Orthogonal Complements
Orthogonal subspaces; examples; nonexample. Orthogonal complements. Trivial observations about orthogonal subspaces and orthogonal complements. Fundamental Subspaces Theorem. More facts about orthogonal complements: the dimension of an orthogonal complement is complementary to the dime
From playlist Course 4: Linear Algebra (Fall 2017)
Linear Algebra: What is a Subspace?
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/
From playlist Basics: Linear Algebra
Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples
A subspace is a subset that respects the two basic operations of linear algebra: vector addition and scalar multiplication. We say they are "closed under vector addition" and "closed under scalar multiplication". On a subspace, you can do linear algebra! Indeed, a subspace is an example of
From playlist Linear Algebra (Full Course)
Subspaces of a vector space. Sums and direct sums.
From playlist Linear Algebra Done Right
What's a subspace of a vector space? How do we check if a subset is a subspace?
From playlist Linear Algebra
A matrix of coefficients, when viewed in column form, is used to create a column space. This is simply the space created by a linear combination of the column vectors. A resulting vector, b, that does not lie in this space will not result in a solution to the linear system. A set of vec
From playlist Introducing linear algebra
Classic linear algebra exercise: the union of a subspace is a subspace if and only if one is contained in the other. This is also good practice with the definition of a subspace, and also shows how to prove statements of the form p implies (q or r) Check out my vector space playlist: http
From playlist Vector Spaces
Math 060 Fall 2017 110317C Direct Sums
Definition of direct sum. Example; nonexample. Theorem: given any subspace S of R^n, we can express R^n as the direct sum of S and S's orthogonal complement. Theorem: the orthogonal complement of the orthogonal complement of a subspace is the subspace. Clarifying the relationship betwe
From playlist Course 4: Linear Algebra (Fall 2017)
Orthogonal complement of the orthogonal complement | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/lin-alg-orthogonal-complement-of-the-orthogonal-complement Finding that the orthogonal complement of the ort
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Examples of sets that are not subspaces and showing why they’re not subspaces Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0 Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
From playlist Matrix Algebra
Representing vectors in rn using subspace members | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/lin-alg-representing-vectors-in-rn-using-subspace-members Showing that any member of Rn can be represented a
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Orthogonal complements. The direct sum of a subspace and its orthogonal complement. Dimension of the orthogonal complement. The orthogonal complement of the orthogonal complement.
From playlist Linear Algebra Done Right
Duality in Linear Algebra: Dual Spaces, Dual Maps, and All That
An exploration of duality in linear algebra, including dual spaces, dual maps, and dual bases, with connections to linear and bilinear forms, adjoints in real and complex inner product spaces, covariance and contravariance, and matrix rank. More videos on linear algebra: https://youtube.c
From playlist Summer of Math Exposition Youtube Videos
Orthogonal complements | Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/othogonal-complements/v/linear-algebra-orthogonal-complements Orthogonal Complements as subspaces. Watch the next lesson: https://w
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
Spectral Theorem for Real Matrices: General nxn Case
Linear Algebra: We state and prove the Spectral Theorem for real vector spaces. That is, if A is a real nxn symmetric matrix, we show that A can be diagonalized using an orthogonal matrix. The proof refers to the 2x2 case and to results from the video Beyond Eigenspaces: Real Invariant
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Karoly Boroczky - Equality in the Reverse Brascamp Lieb Inequality - IPAM at UCLA
Recorded 07 February 2022. Karoly Boroczky of the Renyi Institute of Mathematics presents "Equality in the Reverse Brascamp Lieb Inequality" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The Reverse Brascamp Lieb inequality is a generalization of the Pre
From playlist Workshop: Calculus of Variations in Probability and Geometry
Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=KcI2_r51Eb8&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Another example of a projection matrix | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/alternate-bases/orthogonal-projections/v/lin-alg-another-example-of-a-projection-matrix Figuring out the transformation matrix for a projection onto
From playlist Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
