WHEN LIFE IS LINEAR

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目次

Contents XI Preface . Acknowledgments . ー X Marks the Spot 2 Entermg the Matr1X. 2.1 Sub Swapping 2.2 Spying on the Matr1X 2.3 Math in the Matnx 3 Sum Matr1ces . 3.1 Adding to Things 3.2 Getting lnverted 3.3 Blending Space 3.4 Linearly lnvisible 3.5 Leaving Through a Po 4 Fitting the Norm 4.1 Recommended Movie 4.2 Handwr1ting at a Distance 5 Go Forth and Multiply . 5.1 Scaly by Product 5.2 Computing Similar Taste 5.3 ScaIing to Higher Dimens10ns 5.4 Escher ⅲ the Matnx 5.5 Lamborghini Spinout 5.6 Line Detector . XIII ・ 1 5 ) -6 一 8 0 っ 0 っ 0 - 、 ) -6 8 0- っ 4 4 一 6 9 一 9 一 -0 一 -4 -4 9 一 っ ~ つんっ ~ っ 4 っ ~ っ 4 っ 0 00 、 ) っ 0 -4

6 lt's EIementary, My Dear Watson . 6.1 Visual Operation 6.2 Being Cryptic 7 Math to the Max . 7.1 Dash ofMath 7.2 Linear Path to CoIIege 7.3 Going Cocoa for Math 8 Stretch and Shrmk . 8.1 Getting Some Definition 8.2 Getting Graphic 8.3 Finding Groupies 8.4 Seeing the Pr1ncipal 9 Zombie Math—Decomposing ・ 9.1 A SinguIarly Valuable Matr1X Decomposition 9.2 Feeling Compressed 9.3 ln a Blur 9.4 Losing Some Memory 10 What Are the Chances? . 10.1 Down the Chute 10.2 Google's Rankings of Web Pages IO. 3 EnJOYing the Chaos 1 1 Mining for Meaning . 1 1 」 Slice and Dice 11.2 Movie with not Much Dimens10n 11.3 Presidential Library of Eigenfaces 11.4 Recommendation—Seeing Stars 12 Who's Number 1 ? . 12.1 Getting Massey 12.2 CoIIey Method 12.3 Rating Madness 12.4 March MATHness 12.5 Adding Weight to the Madness に .6 World Cup Rankings 13 End ofthe Line . Bibliography . lndex . Contents 44 46 50 55 55 60 64 69 69 72 76 81 86 88 90 92 92 96 101 . 106 106 . 1 18 119 121 121 123 125 127 . 131 . 133 . 135

addition, い AIdrin, Buzz,16 ASCII art, 5 コ 0--- に Barnsley's fern, 105 Bolt, Usain, 55 BowI Championship Senes, Ⅱ 9 cosine similarity, 32 correlation, 64 , 66 convex combination, Colley method, に一 clustering, 72 ー 76 Chutes and Ladders, 92 chocolate, 64 ー 68 Chartier, Tanya, ⅸ Chartier, Noah, 20 chaos game,103 Caesar cipher, 引 Caesar, Julius, 50 Burke, Tom, 56 Brin, Sergey, 96 Brenkus, John, 59 bracketology, に 3 extended Fiedler method, 川 8 data mining, system Ⅱ 4 cryptography, 50---53 wildcatlogo, 46 MOOC, ⅸ Davidson College similarity measures, 24 , 30 Prmcipal Component Analysis, 80 , lndex eigenfaces, Ⅱ 2 edge detection, 4 ト - ・ 43 downsampling image, 90 dot product, 41, 42 digit recognition, 26--28 diagonal matrix, 82 135 Kozek, Mark,129 Kennedy, J0hn F. コ 6 , Ⅱ 4 Jiuzhang Suanshu, 3 , 44 invert C 司 0 「 S , ー 5 image compression, 86 ー 88 homogeneous coordinates, 36 Hines, Jim, 55 grayscale image, 8 Goog に , 96 Gaussian elimination, 46 ー 50 Frobenius norm, 82 fractal, 101—105 FIFA World Cup, に 7 Fiedler, Miroslav, 74 Fiedler vector, 74 , 75 fangcheng, 44 Facebook, 75 , 川 6 Euclidean norm, 23 Euclidean distance, 32 derivat ion, 69 eigenvalue, 69

136 Lamborghini, 39 L 叩 lacian matrix, 74 , 108 law ofcosines, 引 least-squares e 「「 or , 58 Lewis, Carl, 55 Lincoln, Abraham, 49 linear combination, ー 7 linearleast squares, 55 ーー 68 Liu, Andrew, い 0 Macnamara, Gregory,130 M arch M adness, に 3 Markov chain, 92 ー 1 田 transition matrix, 93 Massey method, Ⅱ 9 Massey, Kenneth, Ⅱ 9 Mathematical Association ofAmenca, Ⅸ Mossinghoff, Michael,130 Mona Lisa, 6 コ 0 , Ⅱコ 4 コ 5 , 48 , 刀 defining, 5 ASCII art, 5 graphing, 9 matnx lndex MovieLens, 25 , 33 multiplication matrix, 34 reflection matrix, 36 rotation matrix, 36 , 39 scalar, い scalar product, 29 Museum Of Mathematics, Netflix, Ⅱ 4 noise, 88 no 「 m Euclidean, 23 , 32 taxicab geometry, 22 tax icab norm, 24 19 / ・ Oak Ridge NationaI Laboratory, 54 Olympic 川 0 meter dash, 55 Page, Larry, 96 Page Rank, 96 ー -1 田 Perron's theorem,100 Wright, Jordan, い 0 Vigen, Tyler, 66 United States Postal Service, 26 し & ルの & わイ R 0 60 ー 64 TSP A コ traveling salesman problem, 1 transpose, 23 supercomputer, 54 sw 叩 ping, 6 submatrix, 5 , に spy 可 0t , 9 Snakes and Ladders, 92 si ngular values, 82 , 89 Frobenius norm, 82 defined, 82 singular value decomposition, 8 レⅵ singleton,109 similarity measures, 24 , 30 Sierpifiski, Waclaw, 102 Sierpifiski's triangle, 川 2 shear mapping, 刀 Schultz, Andrew, 88 scalar product, 4 し 42 residual vector, 58 recommendation system, Ⅱ 4 ーⅡ 7 rank of matrix, 83 quattuorvigintillion, 50 prmcipal components, 76 Principal Component AnaIysis, 76- ー 80 ,

奥付

◎ 2 田 5 by The Mathematical Association of America (lncorporated) Library Of Congress ControI Number: 2014959438 Print edition ISBN: 978-0-88385-649-9 Electronic edition ISBN: 978-0-88385-988-9 Printed in the United States Of America Current Printing (last digit): 10 9 8 7 6 5 4 3 2