Matrix Theory: Let T: R^4 to R^4 be the linear transformation that sends v to Av where A = [0 0 0 -1 \ 1 0 0 0 \ 0 1 0 -2 \ 0 0 1 0]. Find all subspaces invariant under T.
From playlist Matrix Theory
Eva Gallardo Gutiérrez: The invariant subspace problem: a concrete operator theory approach
Abstract: The Invariant Subspace Problem for (separable) Hilbert spaces is a long-standing open question that traces back to Jonhn Von Neumann's works in the fifties asking, in particular, if every bounded linear operator acting on an infinite dimensional separable Hilbert space has a non-
From playlist Analysis and its Applications
Invariant subspaces. Eigenvalues and eigenvectors. A list of eigenvectors correpsonding to distinct eigenvalues is linearly indepenedent. The number of distinct eigenvalues is at most the dimension of the vector space.
From playlist Linear Algebra Done Right
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)
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
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
Subspaces of a vector space. Sums and direct sums.
From playlist Linear Algebra Done Right
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
Representation Theory(Repn Th) 3 by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Beyond Eigenspaces: Real Invariant Planes
Linear Algebra: In the context of real vector spaces, one often needs to work with complex eigenvalues. Let A be a real nxn matrix A. We show that, in R^n, there exists at least one of: an (nonzero) eigenvector for A, or a 2-dimensional subspace (plane) invariant under A.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Positive Semi-Definite Matrix 2: Spectral Theorem
Matrix Theory: Following Part 1, we note the recipe for constructing a (Hermitian) PSD matrix and provide a concrete example of the PSD square root. We prove the Spectral Theorem for C^n in the remaining 9 minutes.
From playlist Matrix Theory
Proof that the Kernel of a Linear Transformation is a Subspace
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Kernel of a Linear Transformation is a Subspace
From playlist Proofs
Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control
This video illustrates the use of the Koopman operator to simulate and control a nonlinear dynamical system using a linear dynamical system on an observable subspace. From the Paper: Koopman observable subspaces and finite linear representations of nonlinear dynamical systems for contro
From playlist Research Abstracts from Brunton Lab
Stefan Teufel: Peierls substitution for magnetic Bloch bands
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
What's a subspace of a vector space? How do we check if a subset is a subspace?
From playlist Linear Algebra
RT1: Representation Theory Basics
Representation Theory: We present basic concepts about the representation theory of finite groups. Representations are defined, as are notions of invariant subspace, irreducibility and full reducibility. For a general finite group G, we suggest an analogue to the finite abelian case, whe
From playlist *** The Good Stuff ***