Coding the Matrix, Linear Algebra through Applications to Computer Science, Klein P.N.

Coding the Matrix, Linear Algebra through Applications to Computer Science, Edition 1,  Klein P.N.

An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics.




Gaussian elimination.
In this chapter, we finally present a sophisticated algorithm for solving computational problems in linear algebra. The method is commonly called Gaussian elimination but was illustrated in Chapter Eight of a Chinese text, The Nine Chapters on the Mathematical Art, that was written roughly two thousand years before Gauss. Many years later, the method was rediscovered in Europe; it was described in full by Isaac Newton and by Michel Rolle, and elaborated by many others. Gauss got into the act in adapting the method to address another computational problem, one we address in Chapter 8.

Contents.
0.The Function (and other mathematical and computational preliminaries).
1.The Field.
2.The Vector.
3.The Vector Space.
4.The Matrix.
5.The Basis.
6.Dimension.
7.Gaussian elimination.
8.The Inner Product.
9.Orthogonalization.
10.Special Bases.
11.The Singular Value Decomposition.
12.The Eigenvector.
13.The Linear Program.



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