notes_1a_matrix - Fall 2004 ICE Topics Process Control by...

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Fall 2004 ICE Topics: Process Control by Design 10.492 Lecture Notes 1a: Brief Guide to Matrices what meaneth we by matrix? A matrix is a 2-dimensional array of things, where these things can be numbers, variables, or math expressions. The matrix is navigated by rows and columns, and we always name the row first when locating any particular element of the matrix. When presenting matrices, we double- underline the summary name A of the matrix, corral the elements in braces, and provide row- column subscripts to locate individual elements. (Regard a ij as the name for some quantity of interest – number, variable, expression.) a 11 a 12 a 13 a 14 A a a 21 a 22 a 23 a 24 31 a 32 a 33 a 34 Matlab indicates an element by putting subscripts in parentheses after the matrix name >> a = [ 1 2 ; 3 4 ] a = 1 2 3 4 >> a(1,2) ans = 2 = A row matrix is a single row, and a column matrix a single column; we collectively call these 1- dimensional matrices “vectors”. We use a single underline for the name. We could still use double R,C subscripts, but I don’t think most people bother with that. x x 11 1 = y = y 11 [ y 12 y 13 ] = [ y 1 3 ] x = y y x x 2 21 2 x x 31 3 In matlab, use the semicolon to make a row shift. >> y = [ 1 2 3 ] y = 1 2 3 >> x = [1; 2; 3 ] x = 1 2 3 revised 2004 Dec 17 Dr. Barry S. Johnston, Copyright 2004. 1
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Fall 2004 ICE Topics: Process Control by Design 10.492 Lecture Notes 1a: Brief Guide to Matrices combining a matrix with a scalar quantity a 12 = ca 11 ca 12 A c = c A = c a 11 ca 21 a 21 a 22 ca 22 c + a 11 c + a 12 a 11 a 12 c + A = A + c = c + = c + a 21 c + a 22 a 21 a 22 adding two matrices (they must be of the same shape) a 11 a 12
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