• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
A Study of Flexible Shoe System for Biped Robot
A Study of Flexible Shoe System for Biped Robot

GROUPS AND THEIR REPRESENTATIONS 1. introduction
GROUPS AND THEIR REPRESENTATIONS 1. introduction

Proof Writing - Middlebury College: Community Home Page
Proof Writing - Middlebury College: Community Home Page

Observable operator models for discrete stochastic time series
Observable operator models for discrete stochastic time series

Powerpoint (recommended)
Powerpoint (recommended)

Math 308, Linear Algebra with Applications
Math 308, Linear Algebra with Applications

THE PROBABILITY OF CHOOSING PRIMITIVE
THE PROBABILITY OF CHOOSING PRIMITIVE

Nonsymmetric algebraic Riccati equations and Wiener
Nonsymmetric algebraic Riccati equations and Wiener

... square matrix A will be denoted by σ(A). The open left half-plane, the open right half-plane, the closed left half-plane and the closed right half-plane will be denoted by C< , C> , C≤ and C≥ , respectively. In [14], iterative methods are studied for the numerical solution of (1.2) with the conditio ...
Chapter 4: Lie Algebras
Chapter 4: Lie Algebras

211 - SCUM – Society of Calgary Undergraduate Mathematics
211 - SCUM – Society of Calgary Undergraduate Mathematics

RT -symmetric Laplace operators on star graphs: real spectrum and self-adjointness
RT -symmetric Laplace operators on star graphs: real spectrum and self-adjointness

Algorithms ・ 6.5 R
Algorithms ・ 6.5 R

Lie Theory, Universal Enveloping Algebras, and the Poincar้
Lie Theory, Universal Enveloping Algebras, and the Poincar้

Computing the Cholesky Factorization of Sparse Matrices
Computing the Cholesky Factorization of Sparse Matrices

... first element with row index larger than j in columnsi , if there is such an element. If not, it is not set (that is, it contains a special invalid value). The other n − j + 1 elements of cursors are not yet used. Like columns, rows is an array of linked list. The ith list stores the elements of Li,1 ...
Linear Algebra Math 308 S. Paul Smith
Linear Algebra Math 308 S. Paul Smith

24. Orthogonal Complements and Gram-Schmidt
24. Orthogonal Complements and Gram-Schmidt

Matrix Lie groups and their Lie algebras
Matrix Lie groups and their Lie algebras

Algorithms 6.5 R
Algorithms 6.5 R

The Power of Depth 2 Circuits over Algebras
The Power of Depth 2 Circuits over Algebras

Chemistry 431 - NC State University
Chemistry 431 - NC State University

Normal Forms and Versa1 Deformations of Linear
Normal Forms and Versa1 Deformations of Linear

... studied problem in many branches of mathematics, the Jordan normal form being the most familiar example in the case where G is the general linear group GL(n, C) and L its Lie algebra gl(n, C). The question of finding normal forms for real linear homogeneous Hamiltonian differential equations with co ...
Computational Aspects of MRI Geometrical Transforms 1
Computational Aspects of MRI Geometrical Transforms 1

Chapter 2 - U.I.U.C. Math
Chapter 2 - U.I.U.C. Math

Algorithms ・ 6.5 R
Algorithms ・ 6.5 R

Algorithms 6.5 R
Algorithms 6.5 R

< 1 ... 12 13 14 15 16 17 18 19 20 ... 112 >

Matrix multiplication

In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. Numbers such as the real or complex numbers can be multiplied according to elementary arithmetic. On the other hand, matrices are arrays of numbers, so there is no unique way to define ""the"" multiplication of matrices. As such, in general the term ""matrix multiplication"" refers to a number of different ways to multiply matrices. The key features of any matrix multiplication include: the number of rows and columns the original matrices have (called the ""size"", ""order"" or ""dimension""), and specifying how the entries of the matrices generate the new matrix.Like vectors, matrices of any size can be multiplied by scalars, which amounts to multiplying every entry of the matrix by the same number. Similar to the entrywise definition of adding or subtracting matrices, multiplication of two matrices of the same size can be defined by multiplying the corresponding entries, and this is known as the Hadamard product. Another definition is the Kronecker product of two matrices, to obtain a block matrix.One can form many other definitions. However, the most useful definition can be motivated by linear equations and linear transformations on vectors, which have numerous applications in applied mathematics, physics, and engineering. This definition is often called the matrix product. In words, if A is an n × m matrix and B is an m × p matrix, their matrix product AB is an n × p matrix, in which the m entries across the rows of A are multiplied with the m entries down the columns of B (the precise definition is below).This definition is not commutative, although it still retains the associative property and is distributive over entrywise addition of matrices. The identity element of the matrix product is the identity matrix (analogous to multiplying numbers by 1), and a square matrix may have an inverse matrix (analogous to the multiplicative inverse of a number). A consequence of the matrix product is determinant multiplicativity. The matrix product is an important operation in linear transformations, matrix groups, and the theory of group representations and irreps.Computing matrix products is both a central operation in many numerical algorithms and potentially time consuming, making it one of the most well-studied problems in numerical computing. Various algorithms have been devised for computing C = AB, especially for large matrices.This article will use the following notational conventions: matrices are represented by capital letters in bold, e.g. A, vectors in lowercase bold, e.g. a, and entries of vectors and matrices are italic (since they are scalars), e.g. A and a. Index notation is often the clearest way to express definitions, and is used as standard in the literature. The i, j entry of matrix A is indicated by (A)ij or Aij, whereas a numerical label (not matrix entries) on a collection of matrices is subscripted only, e.g. A1, A2, etc.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report