Table of Contents

There is also a listing of tables, figures, and captioned examples.

Chapter 1: Introduction

• 1.1 Welcome
• 1.2 Product Features
• 1.3 Products and Services Information

Chapter 2: Class Overview

• 2.1 The Class Concept
• 2.2 Kinds of Classes
• 2.2.1 A Note on Terminology
• 2.3 Class Groups of the Linear Algebra Module
• 2.3.1 Math Vector Classes
• 2.3.2 Sparse Matrix Classes
• 2.3.3 Factorization Classes
• 2.3.4 Symmetric Eigenvalue Decomposition Classes
• 2.3.5 Nonsymmetric Eigenvalue Decomposition Classes
• 2.3.6 Least Squares Factorization Classes
• 2.3.7 Decomposition Classes

Chapter 3: Vectors and Matrices

• 3.1 Defining Vectors
• 3.2 Defining Matrices
• 3.3 Matrix Precision and Shape
• 3.4 Copy Constructors: References and Copies
• 3.5 Accessing Data
• 3.5.1 Individual Elements
• 3.5.2 Bounds Checking
• 3.5.3 Changing Elements with operator()()
• 3.5.4 val() and set()
• 3.5.5 Rows, Columns and Diagonals
• 3.5.6 Components of Complex Matrices
• 3.5.7 Direct Access to Data
• 3.6 Type Conversion
• 3.6.1 Converting Precisions
• 3.6.2 Converting Shapes
• 3.7 Submatrices
• 3.7.1 General Matrices
• 3.7.2 Leading Submatrices

Chapter 4: Factorizations

• 4.1 Defining Factorizations
• 4.2 Solving a System of Equations
• 4.2.1 Error Checking
• 4.3 Solving Several Systems of Equations
• 4.4 Calculating the Determinant, Inverse, and Condition Number
• 4.4.1 Determinants
• 4.4.2 Matrix Inverses
• 4.4.3 Condition Number

Chapter 5: Least Squares Factorizations

• 5.1 Defining the Problem
• 5.2 Solving a Least Squares Problem
• 5.3 Implementations Provided
• 5.4 Solving a Numerically Underdetermined System

Chapter 6: Symmetric Eigenvalue Problems

• 6.1 Defining the Problem
• 6.2 Decomposition Object
• 6.3 Servers
• 6.4 Computing Selected Eigenvalues

Chapter 7: Nonsymmetric Eigenvalue Problems

• 7.1 Defining the Problem
• 7.2 Decomposition Object
• 7.3 Servers
• 7.4 Schur Decompositions
• 7.5 Hessenberg and Balance Decompositions

Chapter 8: Other Decompositions

• 8.1 Kinds of Decompositions
• 8.2 Singular Value Decomposition
• 8.2.1 SVD Server Objects
• 8.3 QR Decomposition and Complete Orthogonal Decomposition
• 8.3.1 Complete Orthogonal Decomposition

Chapter 9: Technical Notes

• 9.1 Function operator()(int, int)
• 9.2 Matrix Entry Helper Classes
• 9.3 Helper Class Member Functions
• 9.4 Basic Linear Algebra Package

Topic Index

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