In linear algebra, a Moore matrix, introduced by E. H. Moore, is a matrix defined over a finite field. When it is a square matrix its determinant is called a Moore determinant (this is unrelated to the Moore determinant of a quaternionic Hermitian matrix). The Moore matrix has successive powers of the Frobenius automorphism applied to its columns (beginning with the zeroth power of the Frobenius automorphism in the first column), so it is an m × n matrix orfor all indices i and j. (Some authors use the transpose of the above matrix.) The Moore determinant of a square Moore matrix (so m = n) can be expressed as: where c runs over a complete set of direction vectors, made specific by having the last non-zero entry equal to 1, i.e., In particular the Moore determinant vanishes if and only if the elements in the left hand column are linearly dependent over the finite field of order q. So it is analogous to the Wronskian of several functions. Dickson used the Moore determinant in finding the modular invariants of the general linear group over a finite field. (Wikipedia).
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
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
Visualization of tensors - part 1
This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor. Future parts of this series will show more theory and more examples. It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'te
From playlist Animated Physics Simulations
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
Random Vectors, Random Matrices, Permuted Products, Permanents, and Diagrammatic Fun - Moore
Cris Moore Santa Fe Institute October 1, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
What is a vector? We gently introduce the i and j basis vectors and the idea of a column vector is presented. The algebra of addition, subtraction and scalar multiplication is discussed. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Take a sh
From playlist Introduction to Vectors
The Moore-Penrose Pseudoinverse — Topic 37 of Machine Learning Foundations
This video introduces Moore-Penrose pseudoinversion, a linear algebra concept that enables us to invert non-square matrices. The pseudoinverse is a critical machine learning concept because it solves for unknown variables within the non-square systems of equations that are common in machin
From playlist Linear Algebra for Machine Learning
This video introduces the identity matrix and illustrates the properties of the identity matrix. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
The Arnold conjecture via Symplectic Field Theory polyfolds -Ben Filippenko
Symplectic Dynamics/Geometry Seminar Topic: The Arnold conjecture via Symplectic Field Theory polyfolds Speaker: Ben Filippenko Affiliation: University of California, Berkeley Date: April 1, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Data-Driven Control: Balancing Example
In this lecture, we give an example of how a change of coordinates can balance the controllability and observability of an input—output system. The example is inspired by the example in Moore’s famous 1981 IEEE TAC paper. https://www.eigensteve.com/
From playlist Data-Driven Control with Machine Learning
Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
GRCon19 - AI and SDR: Software Meets Hardware Again... by Manuel Uhm
AI and SDR: Software Meets Hardware Again... by Manuel Uhm, Jason Vidmar Over the course of the last 30 years, SDR has become the de facto industry standard for the implementation of waveforms for communications, both military and commercial. During that time, the desire for waveforms to
From playlist GRCon 2019
Simon Coste - Trou spectral de matrices de Markov sur des graphes
http://www.lesprobabilitesdedemain.fr/ Organisateurs : Linxiao Chen, Sophie Laruelle, Pascal Maillard, Bastien Mallein, Damien Simon et la Fondation Sciences Mathématiques de Paris Soutiens : LabEx Mathématiques Hadamard et École Doctorale Mathématiques Hadamard.
From playlist Les probabilités de demain 2017
CUDA In Your Python: Effective Parallel Programming on the GPU
It’s 2019, and Moore’s Law is dead. CPU performance is plateauing, but GPUs provide a chance for continued hardware performance gains, if you can structure your programs to make good use of them. In this talk you will learn how to speed up your Python programs using Nvidia’s CUDA platform.
From playlist Machine Learning
From playlist Machine Learning Streams
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)
Augmentations, generating families and micro local sheaves by Michael G Sullivan
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
William Horton: CUDA in Your Python: Effective Parallel Programming on the GPU
It’s 2019, and Moore’s Law is dead. CPU performance is plateauing, but GPUs provide a chance for continued hardware performance gains, if you can structure your programs to make good use of them. In this talk you will learn how to speed up your Python programs using Nvidia’s CUDA platform.
From playlist PyColorado 2019
An Overview of High Performance Computing and Challenges for the Future
Google Tech Talks January, 25 2008 ABSTRACT In this talk we examine how high performance computing has changed over the last 10-year and look toward the future in terms of trends. These changes have had and will continue to have a major impact on our software. A new generation of softwar
From playlist Scientific Computing
The Diagonalization of Matrices
This video explains the process of diagonalization of a matrix.
From playlist The Diagonalization of Matrices