Lectures on Linear Algebra

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Courier Corporation, 1989 - Mathematics - 185 pages
Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.
 

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Contents

nDimensional Spaces Linear and Bilinear Forms
1
Euclidean space
14
Orthogonal basis Isomorphism of Euclidean spaces
21
Bilinear and quadratic forms
34
Reduction of a quadratic form to a sum of squares
42
Reduction of a quadratic form by means of a triangular trans formation
46
The law of inertia
55
Complex ndimensional space
60
Unitary transformations
103
Commutative linear transformations Normal transformations
107
Decomposition of a linear transformation into a product of a unitary and selfadjoint transformation
111
Linear transformations on a real Euclidean space
114
Extremal properties of eigenvalues
126
The Canonical Form of an Arbitrary Linear Transformation
132
Reduction to canonical form
137
Elementary divisors
142

Linear Transformations
70
Invariant subspaces Eigenvalues and eigenvectors of a linear transformation
81
The adjoint of a linear transformation
90
Selfadjoint Hermitian transformations Simultaneous reduc
97
tion of a pair of quadratic forms to a sum of squares
100
Polynomial matrices
149
Introduction to Tensors
164
Tensors
171
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