# Matrices and Linear Transformations

## Cullen, Charles G.

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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.

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Contenuti:

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

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## 1.Matrices and Linear Transformations: Second Edition

ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Paperback. Condizione libro: New. Codice libro della libreria 1172085

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## 2.Matrices and Linear Transformations

Editore: Dover Pubns (1990)
ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Dover Pubns, 1990. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria V0-9780486663289

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## 3.Matrices and Linear Transformations Format: Trade Paper

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Descrizione libro Dover Publishers. Condizione libro: New. Brand New. Codice libro della libreria 0486663280

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## 4.Matrices and Linear Transformations

Editore: Dover Publications Inc. (1991)
ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Dover Publications Inc., 1991. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486663289

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## 5.Matrices and Linear Transformations (Paperback)

Editore: Dover Publications Inc., United States (1991)
ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Dover Publications Inc., United States, 1991. Paperback. Condizione libro: New. 2nd Revised edition. 211 x 135 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAC9780486663289

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## 6.Matrices and Linear Transformations (Paperback)

Editore: Dover Publications Inc., United States (1991)
ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Dover Publications Inc., United States, 1991. Paperback. Condizione libro: New. 2nd Revised edition. 211 x 135 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAC9780486663289

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## 7.Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics)

Editore: Dover Publications (1990)
ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Dover Publications, 1990. Paperback. Condizione libro: New. Codice libro della libreria 0486663280

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## 8.Matrices and Linear Transformations

ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Condizione libro: New. Brand new book, sourced directly from publisher. Dispatched within 2 working days from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-ING-00310355

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## 9.Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics)

Editore: Dover Publications
ISBN 10: 0486663280 ISBN 13: 9780486663289
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Descrizione libro Dover Publications. PAPERBACK. Condizione libro: New. 0486663280 Brand New Book. Ships from the United States. 30 Day Satisfaction Guarantee!. Codice libro della libreria 4800230

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## 10.Matrices and Linear Transformations: Second Edition

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