An enticing advent to vectors and matrices and the algorithms that function on them, meant for the scholar who is aware how one can application. Mathematical ideas and computational difficulties are inspired by means of functions in machine technology. The reader learns via 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 photographs, face detection, encryption and secret-sharing, integer factoring, elimination standpoint from a picture, PageRank (Google's rating algorithm), and melanoma detection from mobilephone positive aspects. A better half site,
codingthematrix.com
presents information and help code. many of the assignments might be auto-graded on-line. Over 200 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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Extra info for Coding the Matrix: Linear Algebra through Applications to Computer Science
425 426 427 428 429 430 430 431 431 432 433 435 437 438 438 nine Orthogonalization nine. 1 Projection orthogonal to a number of vectors . . . . . . . . . . . . . . . . . . . . nine. 1. 1 Orthogonal to a suite of vectors . . . . . . . . . . . . . . . . . . . . . . . nine. 1. 2 Projecting onto and orthogonal to a vector area . . . . . . . . . . . . nine. 1. three First test at projecting orthogonal to a listing of vectors . . . . . . . nine. 2 Projecting orthogonal to jointly orthogonal vectors . . . . . . . . . . . . . . nine. 2. 1 Proving the correctness of venture orthogonal . . . . . . . . . . . . nine. 2. 2 Augmenting undertaking orthogonal . . . . . . . . . . . . . . . . . . . . nine. three development an orthogonal set of turbines . . . . . . . . . . . . . . . . . . . . . nine. three. 1 The orthogonalize method . . . . . . . . . . . . . . . . . . . . . . nine. three. 2 Proving the correctness of orthogonalize . . . . . . . . . . . . . . . . nine. four fixing the Computational challenge closest aspect within the span of many vectors nine. five fixing different difficulties utilizing orthogonalize . . . . . . . . . . . . . . . . . . . nine. five. 1 Computing a foundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine. five. 2 Computing a subset foundation . . . . . . . . . . . . . . . . . . . . . . . . . nine. five. three augmented orthogonalize . . . . . . . . . . . . . . . . . . . . . . . . nine. five. four Algorithms that paintings within the presence of rounding blunders . . . . . . . . nine. 6 Orthogonal supplement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine. 6. 1 Definition of orthogonal supplement . . . . . . . . . . . . . . . . . . . nine. 6. 2 Orthogonal supplement and direct sum . . . . . . . . . . . . . . . . . nine. 6. three basic to a aircraft in R3 given as span or affine hull . . . . . . . . . . nine. 6. four Orthogonal supplement and null area and annihilator . . . . . . . . nine. 6. five general to a aircraft in R3 given by means of an equation . . . . . . . . . . . . . . nine. 6. 6 Computing the orthogonal supplement . . . . . . . . . . . . . . . . . nine. 7 The QR factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine. 7. 1 Orthogonal and column-orthogonal matrices . . . . . . . . . . . . . . . nine. 7. 2 Defining the QR factorization of a matrix . . . . . . . . . . . . . . . . nine. 7. three Requring A to have linearly self sufficient columns . . . . . . . . . . . . nine. eight utilizing the QR factorization to unravel a matrix equation Ax = b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 441 441 442 443 445 446 448 450 450 452 454 455 455 456 456 457 457 457 458 459 460 460 461 462 462 463 463 464 eight. four eight. five eight. 6 eight. three. three Orthogonality estate of the answer to the fireplace engine challenge . . eight. three. four discovering the projection and the nearest element . . . . . . . . . . . . . . eight. three. five way to the fireplace engine challenge . . . . . . . . . . . . . . . . . . . eight. three. 6 *Outer product and projection . . . . . . . . . . . . . . . . . . . . . eight. three. 7 in the direction of fixing the higher-dimensional model . . . . . . . . . . . . Lab: desktop studying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. four. 1 the information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. four. 2 Supervised studying . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. four. three speculation classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. four. four picking out the classifier that minimizes the mistake at the education information eight. four. five Nonlinear optimization through hill-climbing . . . . . . . . . . . . . . . . . eight. four. 6 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eight. four. 7 Gradient descent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . assessment questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . difficulties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x CONTENTS nine. eight. 1 nine. eight. 2 nine. eight. three nine. eight. four The sq. case .