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Matrices and Linear Transformations: Second Edition

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Matrices and Linear Transformations: Second Edition Cover

 

Synopses & Reviews

Publisher Comments:

"Comprehensive . . . an excellent introduction to the subject." — Electronic Engineer's Design Magazine.

This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field.

Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods.

The first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers.

Synopsis:

Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.

Synopsis:

Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.

Synopsis:

Undergraduate-level introduction to linear algebra and matrix theory deals with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Also spectral decomposition, Jordan canonical form, solution of the matrix equation AX=XB, and over 375 problems, many with answers. "Comprehensive." — Electronic Engineer's Design Magazine.

Synopsis:

This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. 12 illustrations. Index.

Description:

Includes bibliographical references (p. 272) and index.

Table of Contents

Chapter I Matrices and Linear Systems

1.1 Introduction

1.2 Fields and number systems

1.3 Matrices

1.4 Matrix addition and scalar multiplication

1.5 Transposition

1.6 Partitioned matrices

1.7 Special kinds of matrices

1.8 Row equivalence

1.9 Elementary matrices and matrix Inverses

1.10 Column equivalence

1.11 Equivalence

Chapter 2 Vector Spaces

2.1 Introduction

2.2 Subspaces

2.3 Linear independence and bases

2.4 The rank of a matrix

2.5 Coordinates and isomorphisms

2.6 Uniqueness theorem for row equivalence.

Chapter 3 Determinants

3.1 Definition of the determinant

3.2 The Laplace expansion

3.3 Adjoints and inverses

3.4 Determinants and rank

Chapter 4 Linear Transformations

4.1 Definition and examples

4.2 Matrix representation

4.3 Products and inverses

4.4 Change of basis and similarity

4.5 Characteristic vectors and characteristic values

4.6 Orthogonality and length

4.7 Gram-Schmidt process

4.8 Schur's theorem and normal matrices

Chapter 5 Similarity: Part I

5.1 The Cayley-Hamilton theorem

5.2 Direct sums and invariant subspaces

5.3 Nilpotent linear operators

5.4 The Jordan canonical form

5.5 Jordan form-continued

5.6 Commutativity (the equation AX = XB)

Chapter 6 Polynomials and Polynomial Matrices

6.1 Introduction and review

6.2 Divisibility and irreducibility

6.3 Lagrange interpolation

6.4 Matrices with polynomial elements

6.5 Equivalence over F[x] .

6.6 Equivalence and similarity

Chapter 7 Similarity: Part II

7.1 Nonderogatory matrices

7.2 Elementary divisors

7.3 The classical canonical form

7.4 Spectral decomposition

7.5 Polar decomposition

Chapter 8 Matrix Analysis

8.1 Sequences and series

8.2 Primary functions

8.3 Matrices of functions

8.4 Systems of linear differential equations

Chapter 9 Numerical Methods

9.1 Introduction

9.2 Exact methods for solving AX = K

9.3 Iterative methods for solving AX = K

9.4 Characteristic values and vectors

Answers to Selected Exercises

Appendix

Glossary of Mathematical Symbols

Index

Product Details

ISBN:
9780486663289
Author:
Cullen, Charles G.
Publisher:
Dover Publications
Author:
Mathematics
Author:
Culten
Location:
New York :
Subject:
Mathematics
Subject:
Matrices
Subject:
Transformations
Subject:
Transformations (mathematics)
Subject:
General Mathematics
Subject:
General-General
Subject:
Mathematics - General
Edition Number:
2
Edition Description:
Second Edition
Series:
Dover Books on Mathematics
Series Volume:
no. 3. Pt. 1-
Publication Date:
19900531
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
336
Dimensions:
8.5 x 5.38 in 0.8 lb

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Matrices and Linear Transformations: Second Edition New Trade Paper
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$17.95 In Stock
Product details 336 pages Dover Publications - English 9780486663289 Reviews:
"Synopsis" by ,
Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.
"Synopsis" by ,
Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.

"Synopsis" by ,
Undergraduate-level introduction to linear algebra and matrix theory deals with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Also spectral decomposition, Jordan canonical form, solution of the matrix equation AX=XB, and over 375 problems, many with answers. "Comprehensive." — Electronic Engineer's Design Magazine.
"Synopsis" by , This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. 12 illustrations. Index.
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