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An attractive creation to vectors and matrices and the algorithms that function on them, meant for the scholar who is familiar with tips to software. Mathematical techniques and computational difficulties are inspired by way of purposes in machine technology. The reader learns by means of doing, writing courses to enforce the mathematical innovations and utilizing them to hold out initiatives and discover the functions. Examples comprise: error-correcting codes, ameliorations in images, face detection, encryption and secret-sharing, integer factoring, removal viewpoint from a picture, PageRank (Google's score algorithm), and melanoma detection from phone gains. A spouse site,

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presents info and aid code. lots of the assignments might be auto-graded on-line. Over 2 hundred illustrations, together with a variety of suitable xkcd comics.

Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The internal Product, Special Bases, The Singular worth Decomposition, The Eigenvector, The Linear Program

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2. four Vector addition . . . . . . . . . . . . . . . . . . . . . . . . . 2. four. 1 Translation and vector addition . . . . . . . . . . . . 2. four. 2 Vector addition is associative and commutative . . . 2. four. three Vectors as arrows . . . . . . . . . . . . . . . . . . . . 2. five Scalar-vector multiplication . . . . . . . . . . . . . . . . . . 2. five. 1 Scaling arrows . . . . . . . . . . . . . . . . . . . . . 2. five. 2 Associativity of scalar-vector multiplication . . . . . 2. five. three Line segments in the course of the beginning . . . . . . . . . . . 2. five. four traces during the beginning . . . . . . . . . . . . . . . . 2. 6 Combining vector addition and scalar multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . forty six forty six forty six forty eight forty eight fifty one fifty one fifty two fifty three fifty four fifty six fifty seven fifty nine 60 sixty one sixty three sixty five sixty six sixty seven sixty seven sixty nine sixty nine sixty nine 70 seventy two seventy four seventy five seventy nine eighty eighty one eighty three eighty three eighty four 86 86 87 88 ninety ninety one ninety two ninety two ninety three ninety four ii CONTENTS 2. 7 2. eight 2. nine 2. 10 2. eleven 2. 12 2. thirteen 2. 6. 1 Line segments and contours that don’t plow through the foundation . . . . . . . . . 2. 6. 2 Distributive legislation for scalar-vector multiplication and vector addition . . 2. 6. three First examine convex combos . . . . . . . . . . . . . . . . . . . . . 2. 6. four First examine aﬃne mixtures . . . . . . . . . . . . . . . . . . . . . . Dictionary-based representations of vectors . . . . . . . . . . . . . . . . . . . . 2. 7. 1 Setter and getter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 7. 2 Scalar-vector multiplication . . . . . . . . . . . . . . . . . . . . . . . . . 2. 7. three Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 7. four Vector unfavourable, invertibility of vector addition, and vector subtraction . Vectors over GF (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. eight. 1 ideal secrecy re-revisited . . . . . . . . . . . . . . . . . . . . . . . . . 2. eight. 2 All-or-nothing secret-sharing utilizing GF (2) . . . . . . . . . . . . . . . . . 2. eight. three lighting Out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dot-product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. nine. 1 overall fee or profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. nine. 2 Linear equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. nine. three Measuring similarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. nine. four Dot-product of vectors over GF (2) . . . . . . . . . . . . . . . . . . . . . 2. nine. five Parity bit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. nine. 6 easy authentication scheme . . . . . . . . . . . . . . . . . . . . . . . . 2. nine. 7 Attacking the straightforward authentication scheme . . . . . . . . . . . . . . . . 2. nine. eight Algebraic houses of the dot-product . . . . . . . . . . . . . . . . . . 2. nine. nine Attacking the straightforward authentication scheme, revisited . . . . . . . . . . Our implementation of Vec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 10. 1 Syntax for manipulating Vecs . . . . . . . . . . . . . . . . . . . . . . . . 2. 10. 2 The implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 10. three utilizing Vecs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 10. four Printing Vecs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 10. five Copying Vecs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. 10. 6 From record to Vec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fixing a triangular procedure of linear equations . . . . . . . . . . . . . . . . . . 2. eleven. 1 Upper-triangular structures . . . . . . . . . . . . . . . . . . . . . . . . . . 2. eleven. 2 Backward substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. eleven. three First implementation of backward substitution . . . . . . . . . . . . . . 2. eleven. four while does the set of rules paintings? . . . . . . . . . . . . . . . . . . . . . . 2. eleven. five Backward substitution with arbitrary-domain vectors .

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