In mathematics, the class of Z-matrices are those matrices whose off-diagonal entries are less than or equal to zero; that is, the matrices of the form: Note that this definition coincides precisely with that of a negated Metzler matrix or quasipositive matrix, thus the term quasinegative matrix appears from time to time in the literature, though this is rare and usually only in contexts where references to quasipositive matrices are made. The Jacobian of a competitive dynamical system is a Z-matrix by definition. Likewise, if the Jacobian of a cooperative dynamical system is J, then (−J) is a Z-matrix. Related classes are L-matrices, M-matrices, P-matrices, Hurwitz matrices and Metzler matrices. L-matrices have the additional property that all diagonal entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a Z-matrix is an M-matrix if it is nonsingular and its inverse is nonnegative. All matrices that are both Z-matrices and P-matrices are nonsingular M-matrices. In the context of quantum complexity theory, these are referred to as stoquastic operators. (Wikipedia).
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)
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 Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist Algebra
Definitions of matrix equality and matrix addition allow us to prove that there's a "zero" matrix: an m by n matrix Z that, when added to any other m by n matrix A, yields A. (We also show that Z is unique.)
From playlist Linear Algebra
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
The matrix of a linear map. Addition of matrices. Scalar multiplication of matrices. The vector space of matrices.
From playlist Linear Algebra Done Right
Vectors, both Algebraically and Geometrically
Learning Objectives: 1) Define a vector algebraically and geometrically 2) Defined scalar multiplication of a vector algebraically and geometrically 3) Define vector addition algebraically and geometrically Note: I labelled a column vector as an nx1 matrix in this video. It would have bee
From playlist Older Linear Algebra Videos
This is the second video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with multiplying two matrices. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
Lecture 0809 Principal Component Analysis algorithm
Machine Learning by Andrew Ng [Coursera] 08-02 Dimensionality Reduction
From playlist Machine Learning by Professor Andrew Ng
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
Dirac's belt trick, Topology, and Spin ½ particles
ANSWERS TO FREQUENTLY ASKED QUESTIONS: https://scholar.harvard.edu/files/noahmiller/files/dirac_belt_trick_faq.pdf This is my submission to 3Blue1Brown's "Summer of Math Exposition 1" #SoME1. In this video, I explain what Dirac's famous belt trick has to do with the topology of rotating s
From playlist Summer of Math Exposition Youtube Videos
Lecture 08-02 Dimensionality Reduction
Machine Learning by Andrew Ng [Coursera] 0806 Motivation I: Data Compression 0807 Motivation II: Data Visualization 0808 Principal Component Analysis problem formulation 0809 Principal Component Analysis algorithm 0810 Reconstruction from compressed representation 0811 Choosing the number
From playlist Machine Learning by Professor Andrew Ng
Introduction to inverse problems - Lakshmivarahan
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
Mod-01 Lec-18 Least Square Approximations :Necessary and Sufficient Conditions
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Linear algebra for Quantum Mechanics
Linear algebra is the branch of mathematics concerning linear equations such as. linear functions and their representations in vector spaces and through matrices. In this video you will learn about #linear #algebra that is used frequently in quantum #mechanics or #quantum #physics. ****
From playlist Quantum Physics
Lecture 3 | The Theoretical Minimum
January 23, 2012 - In this course, world renowned physicist, Leonard Susskind, dives into the fundamentals of classical mechanics and quantum physics. He discovers the link between the two branches of physics and ultimately shows how quantum mechanics grew out of the classical structure. I
From playlist Lecture Collection | The Theoretical Minimum: Quantum Mechanics
Chemistry 107. Inorganic Chemistry. Lecture 03
UCI Chemistry: Inorganic Chemistry (Fall 2014) Lec 03. Inorganic Chemistry -- Representations and Character Tables View the complete course: http://ocw.uci.edu/courses/chem_107_inorganic_chemistry.html Instructor: Matthew D. Law License: Creative Commons CC-BY-SA Terms of Use: http://ocw.
From playlist Chem 107: Week 1
This material covers the definition of a matrix and some related ideas, including the definitions of equality, addition, scalar multiplication, and linear combination of matrices.
From playlist Linear Algebra
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