This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.
Author(s): Thomas S. Shores
Series: Undergraduate Texts in Mathematics
Edition: 2
Publisher: Springer
Year: 2018
Language: English
Commentary: original margins
Pages: 491
Preface
Contents
Linear Systems of Equations
Some Examples
Exercises & Problems
Notation & Review of Numbers
Exercises & Problems
Gaussian Elimination - Basic Ideas
Exercises & Problems
Gaussian Elimination - General Procedure
Exercises & Problems
Applications & Computational Notes
Exercises & Problems
Projects & Reports
Matrix Algebra
Matrix Addition & Scalar Multiplication
Exercises & Problems
Matrix Multiplication
Exercises & Problems
Applications of Matrix Arithmetic
Exercises & Problems
Special Matrices & Transposes
Exercises & Problems
Matrix Inverses
Exercises & Problems
Determinants
Exercises & Problems
Tensor Products
Exercises & Problems
Applications & Computational Notes
Exercises & Problems
Projects & Reports
Vector Spaces
Definitions & Basic Concepts
Exercises & Problems
Subspaces
Exercises & Problems
Linear Combinations
Exercises & Problems
Subspaces associated with Matrices & Operators
Exercises & Problems
Bases & Dimension
Exercises & Problems
Linear Systems revisited
Exercises & Problems
Change of Basis & Linear Operators
Exercises & Problems
Intro to Linear Programming
Exercises & Problems
Applications & Computational Notes
Projects & Reports
Geometrical Aspects of Standard Spaces
Standard Norm & Inner Product
Exercises & Problems
Applications of Norms & Vector Products
Exercises & Problems
Orthogonal & Unitary Matrices
Exercises & Problems
Applications & Computational Notes
Exercises & Problems
Projects & Reports
Eigenvalue Problem
Definitions & Basic Properties
Exercises & Problems
Similarity & Diagonalization
Exercises & Problems
Applications to Discrete Dynamical Systems
Exercises & Problems
Orthogonal Diagonalization
Exercises & Problems
Schur Form & Applications
Exercises & Problems
Singular Value Decomposition
Exercises & Problems
Applications & Computational Notes
Exercises & Problems
Project Topics
Geometrical Aspects of Abstract Spaces
Normed Spaces
Exercises & Problems
Inner Product Spaces
Exercises & Problems
Orthogonal Vectors & Projection
Exercises & Problems
Linear Systems revisited
Exercises & Problems
Operator Norms
Exercises & Problems
Applications & Computational Notes
Projects & Reports
Symbols
Solutions to Selected Exercises
Section 1.1, Page 10
Section 1.2, Page 22
Section 1.3, Page 34
Section 1.4, Page 48
Section 1.5, Page 59
Section 2.1, Page 70
Section 2.2, Page 80
Section 2.3, Page 99
Section 2.4, Page 114
Section 2.5, Page 136
Section 2.6, Page 156
Section 2.7, Page 165
Section 2.8, Page 176
Section 3.1, Page 195
Section 3.2, Page 204
Section 3.3, Page 217
Section 3.4, Page 227
Section 3.5, Page 236
Section 3.6, Page 246
Section 3.7, Page 253
Section 3.8, Page 254
Section 4.1, Page 286
Section 4.2, Page 299
Section 4.3, Page 312
Section 4.4, Page 325
Section 5.1, Page 341
Section 5.2, Page 351
Section 5.3, Page 363
Section 5.4, Page 370
Section 5.5, Page 374
Section 5.6, Page 379
Section 5.7, Page 385
Section 6.1, Page 397
Section 6.2, Page 408
Section 6.3, Page 408
Section 6.4, Page 423
Section 6.5, Page 429
Section 6.6, Page 441
Refs
Index
