Within mathematics, an N×N Euclidean random matrix  is defined with the help of an arbitrary deterministic function f(r, r′) and of N points {ri} randomly distributed in a region V of d-dimensional Euclidean space. The element Aij of the matrix is equal to f(ri, rj): Aij = f(ri, rj). (Wikipedia).
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
Calculating the matrix of a linear transformation with respect to a basis B. Here is the case where the input basis is the same as the output basis. Check out my Vector Space playlist: https://www.youtube.com/watch?v=mU7DHh6KNzI&list=PLJb1qAQIrmmClZt_Jr192Dc_5I2J3vtYB Subscribe to my ch
From playlist Linear Transformations
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
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
Matrix Addition, Subtraction, and Scalar Multiplication
This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
Understanding Matrices and Matrix Notation
In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start
From playlist Mathematics (All Of It)
Concentration of Measure on the Compact Classical Matrix Groups - Elizabeth Meckes
Elizabeth Meckes Case Western Reserve Univ May 20, 2014 For more videos, visit http://video.ias.edu
From playlist Mathematics
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Pierre Youssef: Outliers in sparse Wigner matrices
Given a Wigner matrix with centered bounded entries, we study the effect of sparsity on the extreme eigenvalues. More precisely, multiplying the entries by independent Bernoulli variables with parameter pn, we show that as pn decreases, outliers start emerging in the semi-circular law whic
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
What's a partitioned matrix, and how does it relate to linear systems of equations?
From playlist Linear Algebra
Guillaume Aubrun: Asymptotic tensor powers of Banach spaces
HYBRID EVENT Recorded during the meeting "Randoms Tensors and Related Topics" the March 14, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio
From playlist Analysis and its Applications
Discrete Math - 2.6.1 Matrices and Matrix Operations
Characteristics of a matrix, finding the sum, product and transpose of a matrix. Identity matrix is also introduced. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
From playlist Discrete Math I (Entire Course)
Percolation on Nonamenable Groups, Old And New (Lecture-4) by Tom Hutchcroft
PROGRAM: PROBABILISTIC METHODS IN NEGATIVE CURVATURE (ONLINE) ORGANIZERS: Riddhipratim Basu (ICTS - TIFR, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Mahan M J (TIFR, Mumbai) DATE & TIME: 01 March 2021 to 12 March 2021 VENUE: Online Due to the ongoing COVID pandemic, the meeting will
From playlist Probabilistic Methods in Negative Curvature (Online)
Matrix liberation process - Y. Ueda - Workshop 2 - CEB T3 2017
Yoshimichi Ueda / 24.10.17 Matrix liberation process We introduce a natural random matrix counterpart of the so-called liberation process introduced by Voiculescu in the framework of free probability, and consider its possible LDP in the large N limit. ---------------------------------
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Anna Wienhard (7/29/22): Graph Embeddings in Symmetric Spaces
Abstract: Learning faithful graph representations has become a fundamental intermediary step in a wide range of machine learning applications. We propose the systematic use of symmetric spaces as embedding targets. We use Finsler metrics integrated in a Riemannian optimization scheme, that
From playlist Applied Geometry for Data Sciences 2022
CSE 519 -- Lecture 22, Fall 2020
From playlist CSE 519 -- Fall 2020
Joscha Prochno: The large deviations approach to high-dimensional convex bodies, lecture III
Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast
From playlist Workshop: High dimensional spatial random systems
Barbara Giunti (4/29/21): Average complexity of barcode computation for Vietoris-Rips filtrations
In this talk, we present the first theoretical study of the algorithmic complexity of computing the persistent homology of random Vietoris-Rips filtration. Specifically, we prove upper bounds for the average fill-up (number of non-zero entries) of the boundary matrix after matrix reduction
From playlist Vietoris-Rips Seminar
Example of Skew-Symmetric Matrix
Matrix Theory: Let a be an invertible skew-symmetric matrix of size n. Show that n is even, and then show that A^{-1} is also skew-symmetric. We show the identities (AB)^T = B^T A^T and (AB)^{-1} = B^{-1}A^{-1}.
From playlist Matrix Theory
