Invariant subspace problem

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

Example of Invariant Subspace

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

Subspaces in Machine Learning

From playlist Least-Squares Problems, Linear Algebra, and Machine Learning

Invariant Subspaces

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)

Determine the Fundamental Subspaces of a Matrix (2 by 3)

This video explains how to determine the 4 fundamental subspaces of a matrix.

From playlist Fundamental Subspaces of a Matrix

Union of subspaces

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 092517 Adjoint Matrix, Subspaces

Definition of adjoint matrix. Connection with inverse matrix (via "wrong cofactor lemma"). Example. Subspaces: recall main theorem (how verify a subset is a subspace: check closure under vector space operations). Null space. The null space is a subspace. Example of determining the n

From playlist Course 4: Linear Algebra (Fall 2017)

Representing Data with Bases

From playlist Least-Squares Problems, Linear Algebra, and Machine Learning

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.

Bourgain–Delbaen ℒ_∞-spaces and the scalar-plus-compact property – R. Haydon & S. Argyros – ICM2018

Analysis and Operator Algebras Invited Lecture 8.16 Bourgain–Delbaen ℒ_∞-spaces, the scalar-plus-compact property and related problems Richard Haydon & Spiros Argyros Abstract: We outline a general method of constructing ℒ_∞-spaces, based on the ideas of Bourgain and Delbaen, showing how

From playlist Analysis & Operator Algebras

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

Eva Gallardo-Gutiérrez: Spectral decompositions and an extension of a theorem of Atzmon: ...

Bishop’s operator arose in the fifties as possible candidates for being counterexamples to the Invariant Subspace Problem. Several authors addressed the problem of finding invariant subspaces for some of these operators; but still the general problem is open. In this talk, we shall discuss

From playlist Analysis and its Applications

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

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

Complex Stochastic Models and their Applications by Subhroshekhar Ghosh

PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab

From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY

Determine if W is a Subspace of a Vector Space V

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determine if W is a Subspace of a Vector Space V

From playlist Proofs

Xiaoheng Wang: Density of polynomials with squarefree discriminant

Density of polynomials with squarefree discriminant Speaker: Xiaoheng Wang, Princeton University Date and Time: Wednesday, November 2, 2016 - 2:45pm to 3:45pm Location: Fields Institute, Room 230 Abstract: The problem of the density of squarefree discriminant polynomials is an old one,

From playlist Mathematics