The Theory of Matrices

Front Cover
Courier Dover Publications, 2004 - Mathematics - 110 pages
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This volume offers a concise overview of matrix algebra's many applications, discussing topics of extensive research and supplying proofs. Its contents include reviews of matrices, arrays, and determinants; the characteristic equation; associated integral matrices; equivalence, congruence, and similarity; composition of matrices; matric equations; functions of matrices; and matrices of infinite order. 1946 edition.
  

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Contents

Matrices Arrays and Determinants
1
Total niatric algebra
2
Diagonal and scalar matrices
5
Determinants
6
Properties of determinants
8
Rank and nullity
10
Identities among minors
12
Reducibility
14
Linear form moduls
37
Ideals
38
Equivalence
40
Invariant factors and elementary divisors
43
Factorization of a matrix
44
29 Polynomial domains
45
Equivalent pairs of matrices
48
Automorphic transformations
50

Arrays and determinants of higher dimension
15
Matrices in noncommutative systems
16
The characteristic equation
17
15 Determination of the minimum equation
20
Characteristic roots
22
Conjugate sets
24
Limits for the characteristic roots
25
Characteristic roots of unitary matrices
28
HI Associated Integral Matrices
29
Construction of unimodular matrices
31
Greatest common divisors
35
Congruence
51
33 Matrices with rational integral elements
54
Matrices with elements in a field
56
35 Matrices in an algebraically closed field
60
Hermitian matrices
62
Automorphs
65
Similarity
68
Composition of matrices
81
Matric equations
89
Functions of Matrices
97
Matrices of infinite order
104

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References to this book

Circulant Matrices
Philip J. Davis
No preview available - 1994
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