In mathematics, the spectrum of a matrix is the set of its eigenvalues. More generally, if is a linear operator on any finite-dimensional vector space, its spectrum is the set of scalars such that is not invertible. The determinant of the matrix equals the product of its eigenvalues. Similarly, the trace of the matrix equals the sum of its eigenvalues.From this point of view, we can define the pseudo-determinant for a singular matrix to be the product of its nonzero eigenvalues (the density of multivariate normal distribution will need this quantity). In many applications, such as PageRank, one is interested in the dominant eigenvalue, i.e. that which is largest in absolute value. In other applications, the smallest eigenvalue is important, but in general, the whole spectrum provides valuable information about a matrix. (Wikipedia).
Concept Check: Describe the Range or Image of a Linear Transformation (R3, x to 0)
This video explains how to describe the image or range of a linear transformation.
From playlist Matrix (Linear) Transformations
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Concept Check: Describe the Range or Image of a Linear Transformation (3 by 2)
This video explains how to describe the image or range of a linear transformation.
From playlist Matrix (Linear) Transformations
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
Concept Check: Describe the Range or Image of a Linear Transformation (Line Reflection)
This video explains how to describe the image or range of a linear transformation.
From playlist Matrix (Linear) Transformations
How to Quickly Create a Matrix in GeoGebra; How to Multiply 2 Matrices
Creating a matrix in GeoGebra is EASY. You need to use the LIST icons { }. In GeoGebra, a matrix is actually a sequence of lists within a single list. This video shows how.
From playlist Algebra 1: Dynamic Interactives!
The matrix of a linear map. Addition of matrices. Scalar multiplication of matrices. The vector space of matrices.
From playlist Linear Algebra Done Right
Matrices | Determinant of a Matrix (Part 1) | Don't Memorise
What is the Determinant of a Matrix? Is it unique? What are its applications? In this video, we will learn: 0:00 symbol of the determinant of a matrix 0:34 applications of the determinant of a matrix 0:59 only square matrices have determinant Watch Determinant of a Matrix (Part 2) here
From playlist Matrices
(3.2.3) The Determinant of Square Matrices and Properties
This video defines the determinant of a matrix and explains what a determinant means in terms of mapping and area. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Spectral properties of random perturbations of Toeplitz matrices... by Anirban Basak
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
New Universality in Chaos by Masanori Hanada
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Stéphane Nonennmacher - From Fractal Weyl Laws to spectral questions on sparse directed graphs
https://indico.math.cnrs.fr/event/3475/attachments/2180/2563/Nonnenmacher_GomaxSlides.pdf
From playlist Google matrix: fundamentals, applications and beyond
Spectral Properties of Random Perturbations of Non-self-adjoint Operators by Anirban Basak
ICTS In-house 2022 Organizers: Chandramouli, Omkar, Priyadarshi, Tuneer Date and Time: 20th to 22nd April, 2022 Venue: Ramanujan Hall inhouse@icts.res.in An exclusive three-day event to exchange ideas and research topics amongst members of ICTS.
From playlist ICTS In-house 2022
Laurent Massoulié : Non-backtracking spectrum of random graphs: community detection and ...
Abstract: A non-backtracking walk on a graph is a directed path such that no edge is the inverse of its preceding edge. The non-backtracking matrix of a graph is indexed by its directed edges and can be used to count non-backtracking walks of a given length. It has been used recently in th
From playlist Combinatorics
Andreas LÄUCHLI - Numerical Hamiltonian truncation approach to the \phi^4 theory in 1+1d and beyond
https://indico.math.cnrs.fr/event/2435/
From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”
8ECM Plenary Lecture: Alice Guionnet
From playlist 8ECM Plenary Lectures
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
Matrices lesson 1 - What is a matrix, dimension of a matrix, elements of a matrix.
In this lesson we introduce you to the idea of matrices (an object containing an array of numbers). We also talk about some properties / features of matrices.
From playlist Maths C / Specialist Course, Grade 11/12, High School, Queensland, Australia
Hermann Schulz-Baldes: Computational K-theory via the spectral localizer.
Talk by Hermann Schulz-Baldes in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 24, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)