Applied Linear Algebra and Matrix Analysis
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. The student will develop a solid foundation in the following topics: Gaussian elimination and other operations with matrices, basic properties of matrix and determinant algebra, standard Euclidean spaces, both real and complex, geometrical aspects of vectors, such as norm, dot product, and angle, eigenvalues, eigenvectors, and discrete dynamical systems, general norm and inner-product concepts for abstract vector spaces.

For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable.

About the Author:
Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln

1127744539
Applied Linear Algebra and Matrix Analysis
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. The student will develop a solid foundation in the following topics: Gaussian elimination and other operations with matrices, basic properties of matrix and determinant algebra, standard Euclidean spaces, both real and complex, geometrical aspects of vectors, such as norm, dot product, and angle, eigenvalues, eigenvectors, and discrete dynamical systems, general norm and inner-product concepts for abstract vector spaces.

For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable.

About the Author:
Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln

44.99 In Stock
Applied Linear Algebra and Matrix Analysis

Applied Linear Algebra and Matrix Analysis

by Thomas S. Shores
Applied Linear Algebra and Matrix Analysis

Applied Linear Algebra and Matrix Analysis

by Thomas S. Shores

eBook2nd ed. 2018 (2nd ed. 2018)

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Overview

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. The student will develop a solid foundation in the following topics: Gaussian elimination and other operations with matrices, basic properties of matrix and determinant algebra, standard Euclidean spaces, both real and complex, geometrical aspects of vectors, such as norm, dot product, and angle, eigenvalues, eigenvectors, and discrete dynamical systems, general norm and inner-product concepts for abstract vector spaces.

For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable.

About the Author:
Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln


Product Details

ISBN-13: 9783319747484
Publisher: Springer International Publishing
Publication date: 05/02/2018
Series: Undergraduate Texts in Mathematics
Sold by: Barnes & Noble
Format: eBook
File size: 38 MB
Note: This product may take a few minutes to download.

About the Author

Thomas S. Shores is Professor Emeritus of Mathematics at the University of Nebraska–Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.

Table of Contents


Linear Systems of Equations     1
Some Examples     1
Notation and a Review of Numbers     9
Gaussian Elimination: Basic Ideas     21
Gaussian Elimination: General Procedure     33
Computational Notes and Projects     46
Matrix Algebra     55
Matrix Addition and Scalar Multiplication     55
Matrix Multiplication     62
Applications of Matrix Arithmetic     71
Special Matrices and Transposes     86
Matrix Inverses     101
Basic Properties of Determinants     114
Computational Notes and Projects     129
Vector Spaces     145
Definitions and Basic Concepts     145
Subspaces     161
Linear Combinations     170
Subspaces Associated with Matrices and Operators     183
Bases and Dimension     191
Linear Systems Revisited     198
Computational Notes and Projects     208
Geometrical Aspects of Standard Spaces     211
Standard Norm and Inner Product     211
Applications of Norms and Inner Products     221
Orthogonal and Unitary Matrices     233
Change of Basis and LinearOperators     242
Computational Notes and Projects     247
The Eigenvalue Problem     251
Definitions and Basic Properties     251
Similarity and Diagonalization     263
Applications to Discrete Dynamical Systems     272
Orthogonal Diagonalization     282
Schur Form and Applications     287
The Singular Value Decomposition     291
Computational Notes and Projects     294
Geometrical Aspects of Abstract Spaces     305
Normed Spaces     305
Inner Product Spaces     312
Gram-Schmidt Algorithm     323
Linear Systems Revisited     333
Operator Norms     342
Computational Notes and Projects     348
Table of Symbols     355
Solutions to Selected Exercises     357
References     375
Index     377
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