Part III: A Matrix Package

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	Java Number Cruncher: The Java Programmer's Guide to Numerical Computing By Ronald  Mak
	Table of Contents

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This part of the book incrementally develops a practical matrix package. We can then import the classes of this package into any Java application that uses matrices.

Chapter 9 develops the matrix class for the basic operations of addition, subtraction, and multiplication. It also covers subclasses for vectors and square matrices. The chapter's interactive demo uses graphic transformation matrices to animate a three-dimensional wire-frame cube.

Chapter 10 first reviews the manual procedure we learned in high school to solve systems of linear equations. It then introduces LU decomposition to solve linear systems using matrices. An interactive demo creates polynomial regression functions of any order from 1 through 9, which requires solving a system of "normal" equations.

Finally, Chapter 11 uses LU decomposition to compute the inverse of a matrix efficiently and reliably. A demo program tests how well we can invert the dreaded Hilbert matrices, which are notoriously difficult to invert accurately. The chapter also computes determinants and condition numbers of matrices, and it compares different algorithms for solving linear systems.

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