Finite-Dimensional Linear Algebra

Finite-Dimensional Linear Algebra

Author: Mark S. Gockenbach

Publisher: CRC Press

ISBN: 9781439815649

Category: Mathematics

Page: 672

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Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation. The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra). Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.
Finite-Dimensional Linear Algebra
Language: en
Pages: 672
Authors: Mark S. Gockenbach
Categories: Mathematics
Type: BOOK - Published: 2011-06-15 - Publisher: CRC Press

Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation. The author begins with an overview of
Idempotent Analysis and Its Applications
Language: en
Pages: 305
Authors: Vassili N. Kolokoltsov, Victor P. Maslov
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

The first chapter deals with idempotent analysis per se . To make the pres- tation self-contained, in the first two sections we define idempotent semirings, give a concise exposition of idempotent linear algebra, and survey some of its applications. Idempotent linear algebra studies the properties of the semirn- ules An
Mathematics and Its History
Language: en
Pages: 544
Authors: John Stillwell
Categories: Mathematics
Type: BOOK - Published: 2004-01-27 - Publisher: Springer Science & Business Media

This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added as
Discrete Structures and Their Interactions
Language: en
Pages: 224
Authors: Jason I. Brown
Categories: Computers
Type: BOOK - Published: 2016-04-19 - Publisher: CRC Press

Discover the Connections between Different Structures and FieldsDiscrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics,
Foundations of Discrete Mathematics
Language: en
Pages: 748
Authors: K. D. Joshi
Categories: Combinatorial analysis
Type: BOOK - Published: 1989 - Publisher: New Age International

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate