Download E-books Coding the Matrix: Linear Algebra through Applications to Computer Science PDF

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,

codingthematrix.com

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

Show description

Read or Download Coding the Matrix: Linear Algebra through Applications to Computer Science PDF

Similar Linear books

Functional Analysis in Modern Applied Mathematics

During this booklet, we examine theoretical and sensible elements of computing equipment for mathematical modelling of nonlinear structures. a few computing ideas are thought of, similar to equipment of operator approximation with any given accuracy; operator interpolation innovations together with a non-Lagrange interpolation; tools of procedure illustration topic to constraints linked to ideas of causality, reminiscence and stationarity; tools of process illustration with an accuracy that's the most sensible inside of a given category of types; tools of covariance matrix estimation;methods for low-rank matrix approximations; hybrid tools in response to a mix of iterative techniques and top operator approximation; andmethods for info compression and filtering below filter out version should still fulfill regulations linked to causality and varieties of reminiscence.

The Theory of Matrices, Second Edition: With Applications (Computer Science and Scientific Computing)

During this ebook the authors try and bridge the distance among the remedies of matrix idea and linear algebra. it truly is geared toward graduate and complicated undergraduate scholars looking a starting place in arithmetic, laptop technology, or engineering. it's going to even be worthwhile as a reference e-book for these engaged on matrices and linear algebra to be used of their medical paintings.

The Structure of Groups of Prime Power Order

The coclass venture (1980-1994) supplied a brand new and robust strategy to classify finite p-groups. This monograph provides a coherent account of the pondering out of which constructed the philosophy that result in this class. The authors offer a cautious precis and rationalization of the various and tough unique study papers at the coclass conjecture and the constitution theorem, therefore elucidating the history examine for these new to the realm in addition to for skilled researchers.

Extra info for Coding the Matrix: Linear Algebra through Applications to Computer Science

Show sample text content

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 .

Rated 4.80 of 5 – based on 11 votes