Title:

Matrices and linear transformations

Author:

Cullen, Charles G.

Personal Author:

Edition:

Second edition.

Publication Information:

New York : Dover, 1990.

©1972

Physical Description:

xii, 318 pages : illustrations ; 22 cm

General Note:

"An unabridged, corrected republication of the second edition (1972) of the work originally published in 1966 by Addison-Wesley Publishing Company"--T.p. verso.

Language:

English

ISBN:

9780486663289

Format :

Book

### Available:*

Library | Call Number | Material Type | Home Location | Status |
---|---|---|---|---|

Central Library | QA188 .C85 1972 | Adult Non-Fiction | Non-Fiction Area | Searching... |

### On Order

### Summary

### Summary

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.

### 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 |