Lectures on Linear Algebra

ISBN-10: 0486660826

ISBN-13: 9780486660820

Edition: 1989

Authors: I. M. Gel'fand

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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, introduction to tensors, more. Not designed as an introductory text. 1961 edition.
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Book details

List price: $11.95
Copyright year: 1989
Publisher: Dover Publications, Incorporated
Publication date: 9/1/1989
Binding: Paperback
Pages: 185
Size: 5.50" wide x 8.50" long x 0.50" tall
Weight: 0.484
Language: English

n-Dimensional Spaces
Linear and Bilinear Forms
n-Dimensional vector spaces
Euclidean space
Orthogonal basis
Isomorphism of Euclidean spaces
Bilinear and quadratic forms
Reduction of a quadratic form to a sum of squares
Reduction of a quadratic form by means of a triangular transformation
The law of inertia
Complex n-dimensional space
Linear Transformations
Linear transformations
Operations on linear transformations
Invariant subspaces
Eigenvalues and eigenvectors of a linear transformation
The adjoint of a linear transformation
Self-adjoint (Hermitian) transformations
Simultaneous reduction of a pair of quadratic forms to a sum of squares
Unitary transformations
Commutative linear transformations
Normal transformations
Decomposition of a linear transformation into a product of a unitary and self-adjoint transformation
Linear transformations on a real Euclidean space
External properties of eigenvalues
The Canonical Form of an Arbitrary Linear Transformation
The canonical form of a linear transformation
Reduction to canonical form
Elementary divisors
Polynomial matrices
Introduction to Tensors
The dual space
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