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week6_matrix_intro

# week6_matrix_intro - Matrices Foodforthought m=numberofrows...

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9/14/2011 1 Food for thought. . Abraham Lincoln quotes: “I will prepare and some day my chance will come.” “If I had eight hours to chop down a tree, I’d spend six sharpening my axe.” Matrices A matrix is a rectangular array of numbers [A] mxn m = number of rows n = number of columns Examples: [B] 3x1 = 3 2 1 “column” matrix [C] 1x4 = 19 2 6 1 “row” matrix [D] 4x3 = 11 5 25 102 16 2 99 26 54 0 14 12 [E] 3x3 =  1 7 9 4 8 6 2 5 3 . “square” matrix n = m Matrices Index Notation a ij = an element of [A] i= row index j = column index [D] 4x3 = 11 5 25 102 16 2 99 26 54 0 14 12 d 23 = 99 d 12 = 14 d 21 = 54, etc. 43 42 41 33 32 31 23 22 21 13 12 11 d d d d d d d d d d d d General nxm matrix: mn m m n n a a a a a a a a a ... . . ... ... 2 1 2 22 21 1 12 11 Special Square Matrices [A] = 1 0 0 0 8 0 0 0 3 “diagonal” matrix, a ij = 0 if i j [ I ]= 1 0 0 0 1 0 0 0 1 “identity” matrix [U] = 1 0 0 5 8 0 12 4 3 “upper triangular” matrix [L] = 1 6 12 0 8 5 . 0 0 3 “lower triangular” matrix Special Matrices [T] = 44 43 34 33 32 23 22 21 12 11 0 0 0 0 0 0 a a a a a a a a a a “tridiagonal” matrix Matrix Operations Addition/Subtraction If [C] m1xn1 = [A] m2xn2 ±[B] m3xn3 c ij = a ij + b ij Can be performed only between matrices of the same dimensions!

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week6_matrix_intro - Matrices Foodforthought m=numberofrows...

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