Linear Algebra and Its Applications

ISBN-10: 0030105676
ISBN-13: 9780030105678
Edition: 4th 2006
Authors: Gilbert Strang
List price: $311.95 Buy it from $19.20
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Description: Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on  More...

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Book details

List price: $311.95
Edition: 4th
Copyright year: 2006
Publisher: Brooks/Cole
Publication date: 7/19/2005
Binding: Hardcover
Pages: 496
Size: 7.25" wide x 9.25" long x 1.00" tall
Weight: 1.936
Language: English

Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

Matrices and Gaussian Elimination
Introduction
The Geometry of Linear Equations
An Example of Gaussian Elimination
Matrix Notation and Matrix Multiplication
Triangular Factors and Row Exchanges
Inverses and Transposes
Special Matrices and Applications
Review Exercises: Chapter 1
Vector Spaces
Vector Spaces and Subspaces
Solving Ax = 0 and Ax = b
Linear Independence, Basis, and Dimension
The Four Fundamental Subspaces
Graphs and Networks
Linear Transformations
Review Exercises: Chapter 2
Orthogonality
Orthogonal Vectors and Subspaces
Cosines and Projections onto Lines
Projections and Least Squares
Orthogonal Bases and Gram-Schmidt
The Fast Fourier Transform
Review Exercises: Chapter 3
Determinants
Introduction
Properties of the Determinant
Formulas for the Determinant
Applications of Determinants
Review Exercises: Chapter 4
Eigenvalues and Eigenvectors
Introduction
Diagonalization of a Matrix
Difference Equations and Powers A[superscript k]
Differential Equations and e[superscript At]
Complex Matrices
Similarity Transformations
Review Exercises: Chapter 5
Positive Definite Matrices
Minima, Maxima, and Saddle Points
Tests for Positive Definiteness
Singular Value Decomposition
Minimum Principles
The Finite Element Method
Computations with Matrices
Introduction
Matrix Norm and Condition Number
Computation of Eigenvalues
Iterative Methods for Ax = b
Linear Programming and Game Theory
Linear Inequalities
The Simplex Method
The Dual Problem
Network Models
Game Theory
Intersection, Sum, and Product of Spaces
The Jordan Form
Solutions to Selected Exercises
Matrix Factorizations

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