matrix multiplication


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"Matrix multiplication" Introduction


From   Wikipedia , TutorVista
Wikipedia
matrix multiplication : In mathematics, matrix multiplication is the operation of multiplying a matrix with either a scalar or another matrix. This article gives an overview of the various ways to perform matrix multiplication. The ordinary matrix product is the most often used and the most important way to multiply matrices. It is defined between two matrices only if the width of the first matrix equals the height of the second matrix. Multiplying an m × n matrix with an n × p matrix results in an m × p matrix. If many matrices are multiplied together, and their dimensions are written in a list in order, e.g. m × n, n × p, p × q, q × r, the size of the result is given by the first and the last numbers ( m × r), and the values surrounding each comma must match for the result to be defined. The ordinary matrix product is not commutative. An individual element x_{3,4} of the matrix product:= \begin{bmatrix} \cdot & \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot &..   More from Wikipedia

matrix multiplication : Matrix chain multiplication is an optimization problem that can be solved using dynamic programming. Given a sequence of matrices, we want to find the most efficient way to multiply these matrices together. The problem is not actually to perform the multiplications, but merely to decide in which..   More from Wikipedia

Properties of Matrix Multiplication
Matrix multiplication is not commutative in general. Matrix multiplication is associative i.e., (AB)C = A(BC), whenever both sides are defined. Matrix multiplication is distributive over matrix addition i.e., (i) A(B +..
Multiplication of a matrix by a scalar
Let A=[a i j ] be an m x n matrix and k be any number called a scalar. Then the matrix obtained by multiplying every element of A by k is called the scalar multiple of A by k and is denoted by kA. Thus, kA = [k a i j ] m x ..

"Matrix multiplication" Videos


From   Youtube
  Multiplying two 2x2 matrices.
  Multiplying Matrices - Two examples of multiplying a matrix by another matrix are shown. For more free math videos, visit JustMathTutoring.com Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor Austin Math Tutor, Austin Math Tutoring, Austin Algebra... ... math matrix matrice multiplying matrices algebra austin tutor linear SAT ACT AP BC justmathtutoring.com education

"Matrix multiplication" Questions & Answers


From   Yahoo Answers
Question : if i have a time matrix in minutes, and i have to use matrix multiplication to convert it to hours, what would i multiply the matrix by?

Answer : A matrix with only 1/60 along the diagonal...   More from Yahoo Answers

Question : what would be wrong with defining matrix multiplication for matrices for the same size by them entry-by-entry,as with addition and subtraction?

Answer : A very natural question; forgive me if I redirect you to a previous answer I made in the link below :) To make a long story short: there is nothing wrong with that definition of matrix multiplication--- it is in use, although it is often given a different name to distinguish it from what is more commonly meant by "matrix product." The reason the more common meaning of matrix product is what it is is that very often we think of matrices as functions, and the standard matrix product corresponds to function composition (the entrywise product does not)...   More from Yahoo Answers

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