3 3 Matrices - Math - The University of Utah
We call this matrix the 3 ⇥ 3 identity matrix ***** *** Matrix multiplication You can “multiply” two 3⇥3matricestoobtainanother3⇥3matrix Order the columns of a matrix from left to right, so that the 1st column is on the left, the 2nd column is directly to the right of the 1st,andthe3rd column is to the right of the 2nd
Nur Dean - City University of New York
Parallel Algorithms for Matrix Multiplication Example 3x3 Fox’s Algorithm Stage 2: Process (i;(i + 2) mod3) Broadcast along row i (0,2) a 02 (1,0) a 10 (2,1) a 21 a 02;b 20 a 02;b 21 a 02;b 22 a 10;b 00 a 10;b 01 a 10;b 02 a 21 01
Matrix Multiplication : When the number of columns of the first
matrix is the same as the number of rows in the second matrix then matrix multiplication can be performed Here is an example of matrix multiplication for two 2x2 matrices Here is an example of matrices multiplication for a 3x3 matrix When A has dimensions mxn, B has dimensions nxp Then the product of A and B is the matrix C, which has
Systolic Architectures - Computer Action Team
3x3 Systolic Array Matrix Multiplication b2,2 b2,1 b1,2 b2,0 b1,1 b0,2 b1,0 b0,1 b0,0 a0,2 a0,1 a0,0 a1,2 a1,1 a1,0 a2,2 a2,1 a2,0 Alignments in time • Processors arranged in a 2-D grid • Each processor accumulates one element of the product Rows of A Columns of B T = 0
Matrix Multiplication - Oakland University
answer is located on the matrix by the LED’s displaying the position on the matrix I INTRODUCTION For our ECE 378 we have decided to make a 2 x 2 matrix multiplier and a 3 x 3 matrix multiplier A matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix While a matrix are
Matrix Multiplication - University of Plymouth
Section 3: Matrix Multiplication 2 9 3 Matrix Multiplication 2 The extension of the concept of matrix multiplication to matrices, A, B, in which A has more than one row and B has more than one column is now possible The product matrix AB will have the same number of columns as B and each column is obtained by taking the
Matrix multiplication
Matrix multiplication 3x4 matrix 4x2 matrix The multiplication is legal since 2 3 4 5 1 3 number of columns of A is the
Matrices, transposes, and inverses
Feb 01, 2012 · Matrix multiplication For m x n matrix A and n x p matrix B, the matrix product AB is an m x p matrix “outer” parameters become parameters of matrix AB What sizes of matrices can be multiplied together? If A is a square matrix and k is a positive integer, we define Ak = A · A···A k factors Properties of matrix multiplication
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BasicMathematics
MatrixMultiplication
R Horan & M LavelleTheaim of this document is to provide a short, self assessment programme for students who wish to learn how to multiply matrices.Copyright c?2005Email: rhoran,mlavelle@plymouth.ac.ukLastRevision Date: November 2, 2005Version 1.0
Table of Contents
1.Introduction
2.Matrix Multiplication 1
3.Matrix Multiplication 2
4.The Identity Matrix
5.Quiz on Matrix Multiplication
Solutions to Exercises
Solutions to Quizzes
The full range of these packages and some instructions, should they be required, can be obtained from our web pageMathematics Support Materials.Section 1: Introduction 3
1. Introduction
In the packageIntroduction to Matricesthe basic rules ofaddi- tionandsubtractionof matrices, as well asscalar multiplication, were introduced. The rule for themultiplication of two matricesis the subject of this package. The first example is the simplest. Recall that ifMis a matrix then the transpose ofM, written M T, is the matrix obtained fromMby writing the rows ofMas the columns ofM T.IfA= (a1a2... an)is a1×n(row) matrix andB= (b1b2... bn)Tis an×1(column) matrix then the productABis defined as
AB=(a1a2... an)(
((b 1 b2···b
n) ))=a 1b 1+a 2b2+···+a
nb nThis general rule is sometimes called theinner product. N.B.Therow matrixis on the left and thecolumn matrixis on the right.Section 1: Introduction 4
Example 1In each of the following cases, find the productAB. (a)A= (1 2),B= (4 3)T.(b)A= (1 1 1),B= (2 3 4)T. (c)A= (1-1 2 3),B= (1 1-3 2)T.Solution
(a)AB=(1 2)? 43?=1×4 +2×3 = 4 + 6 = 10.
(b)AB=(1 1 1)( (2 3 4) )=1×2 +1×3 +1×4 = 2 + 3 + 4 = 9. (c)AB=(1-1 2 3)( ((1 1 -3 2) ))=1×1 +1×(-1) +2×(-3) +3×2= 1 + (-1) + (-6) + 6 = 0.Section 1: Introduction 5
Exercise 1.For each of the cases below, calculateAB. (Click on the greenletters for solutions.) (a)A= (-2 4),B= (3 2)T, (b)A= (5 3-2),B= (3-4 2)T, (c)A= (4 4-2-3),B= (5-4 32)T.The following observations are worth noting.•The row matrix is on the left, the column matrix is on the right.
•Therowandcolumnhave the same number of elements. •The inner productABis a1×1matrix, i.e. anumber. •Nothing has yet been said about a matrix productBA. QuizIfA= (x x1)andB= (x6 9)T, which of the following values ofxwill result inAB= 0? (a)x= 1,(b)x= 3,(c)x=-3,(d)x=-2.