Cover image for Matrices and linear transformations
Matrices and linear transformations
Cullen, Charles G.
Personal Author:
Second edition.
Publication Information:
New York : Dover, 1990.

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.
Format :


Call Number
Material Type
Home Location
Central Library QA188 .C85 1972 Adult Non-Fiction Non-Fiction Area

On Order



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
Glossary of Mathematical Symbols

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