Determinant of an Operator and of a Matrix
Determinant of an operator. An operator is not invertible if and only if its determinant equals 0. Formula for the characteristic polynomial in terms of determinants. Determinant of a matrix. Connection between the two notions of determinant.
From playlist Linear Algebra Done Right
The identity operator plus a nilpotent operator has a square root. An invertible operator on a finite-dimensional complex vector space has a square root.
From playlist Linear Algebra Done Right
Every operator on a finite-dimensional complex vector space has an upper-triangular matrix with respect to some basis. The eigenvalues of the operator are the numbers along the diagonal of this upper-triangular matrix.
From playlist Linear Algebra Done Right
The complexification of a real vector space. The complexification of an operator on a real vector space. Every operator on a nonzero finite-dimensional real vector space has an invariant subspace of dimension 1 or 2. Every operator on an odd-dimensional real vector space has an eigenvalue.
From playlist Linear Algebra Done Right
Polynomials applied to an operator. Proof that every operator on a finite-dimensional, nonzero, complex vector space has an eigenvalue (without using determinants!).
From playlist Linear Algebra Done Right
Cristina Câmara: Truncated Toeplitz operators
Abstract: Toeplitz matrices and operators constitute one of the most important and widely studied classes of non-self-adjoint operators. In this talk we consider truncated Toeplitz operators, a natural generalisation of finite Toeplitz matrices. They appear in various contexts, such as the
From playlist Analysis and its Applications
Positive operators. Square roots of operators. Characterization of positive operators. Each positive operator has a unique positive square root.
From playlist Linear Algebra Done Right
Abonniert den Kanal, damit er auch in Zukunft bestehen kann. Es ist vollkommen kostenlos und ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erzähle ich ein wenig über lineare Operatoren zwischen normierten Räumen (oder Hilberträumen) und gebe die wichtige Definition
From playlist Funktionalanalysis
Decomposition Via Generalized Eigenvectors
Decomposition of an operator on a complex vector space. For each operator on a complex vector space, there is a basis of the vector space consisting of generalized eigenvectors of the operator. Multiplicity (also called algebraic multiplicity) and geometry multiplicity of an eigenvalue. T
From playlist Linear Algebra Done Right
Jens Kaad: Differentiable absorption of Hilbert C*-modules
The Kasparov absorption (or stabilization) theorem states that any countably generated Hilbert C^*-module is isomorphic to a direct summand in a standard module. In this talk, I will generalize this result by incorporating a densely defined derivation on the base C^*-algebra. The extra com
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Background material on the Cauchy-Riemann equations (Lecture 1) by Debraj Chakrabarti
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Adam Skalski: Translation invariant noncommutative Dirichlet forms
Talk by Adam Skalski in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on April 28, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Lara Ismert: "Heisenberg Pairs on Hilbert C*-modules"
Actions of Tensor Categories on C*-algebras 2021 "Heisenberg Pairs on Hilbert C*-modules" Lara Ismert - Embry-Riddle Aeronautical University, Mathematics Abstract: Roughly speaking, a Heisenberg pair on a Hilbert space is a pair of self-adjoint operators (A,B) which satisfy the Heisenber
From playlist Actions of Tensor Categories on C*-algebras 2021
Josef Teichmann: An elementary proof of the reconstruction theorem
CIRM VIRTUAL EVENT Recorded during the meeting "Pathwise Stochastic Analysis and Applications" the March 09, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Virtual Conference
Lieven Vandenberghe: "Bregman proximal methods for semidefinite optimization."
Intersections between Control, Learning and Optimization 2020 "Bregman proximal methods for semidefinite optimization." Lieven Vandenberghe - University of California, Los Angeles (UCLA) Abstract: We discuss first-order methods for semidefinite optimization, based on non-Euclidean projec
From playlist Intersections between Control, Learning and Optimization 2020
Dynamic equations on time scales
An introductory presentation on dynamic equations on time scales and uniqueness of solutions including new research resutls. The basic ideas of time scale calculus are presented and then a new theorem is discussed under which general initial value problems have, at most, one solution. T
From playlist Mathematical analysis and applications
Chris WENDL - 2/3 Classical transversality methods in SFT
In this talk I will discuss two transversality results that are standard but perhaps not so widely understood: (1) Dragnev's theorem that somewhere injective curves in symplectizations are regular for generic translation-invariant J, and (2) my theorem on automatic transversality in 4-dime
From playlist 2015 Summer School on Moduli Problems in Symplectic Geometry
Koen van den Dungen: Indefinite spectral triples and foliations of spacetime
Motivated by Dirac operators on Lorentzian manifolds, we propose a new framework to deal with non-symmetric and non-elliptic operators in noncommutative geometry. We provide a definition for indefinite spectral triples, and show that these correspond bijectively with certain pairs of spect
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Uniform p-adic wave front sets and zero loci of function ...- R.Cluckers - Workshop 2 - CEB T1 2018
Raf Cluckers (CNRS – Université de Lille & KU Leuven) / 08.03.2018 Uniform p-adic wave front sets and zero loci of functions of C exp-class. I will recall some concrete parts of the course on motivic integration given at the IHP by Halupczok, and use it to define distributions of Cexp cl
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Schemes 46: Differential operators
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin
From playlist Algebraic geometry II: Schemes