Book:I.M. Gel'fand/Lectures on Linear Algebra/Second Edition

I.M. Gel'fand: Lectures on Linear Algebra (2nd Edition)

Published $\text {1961}$, Dover Publications

ISBN 0-486-66082-6 (translated by A. Shenitzer)

Subject Matter

• Linear Algebra

Contents

Preface to the Second Edition (September 1950)

Preface to the First Edition (January 1948)

$\text {I}$. $n$-Dimensional Spaces. Linear and Bilinear Forms

$\S 1$. $n$-Dimensional vector spaces

$\S 2$. Euclidean space

$\S 3$. Orthogonal basis. Isomorphism of Euclidean spaces

$\S 4$. Bilinear and quadratic forms

$\S 5$. Reduction of a quadratic form to a sum of squares

$\S 6$. Reduction of a quadratic form by means of a triangular transformation

$\S 7$. The law of inertia

$\S 8$. Complex $n$-dimensional space

$\text {II}$. Linear Transformations

$\S 9$. Linear transformations. Operations on linear transformations

$\S 10$. Invariant subspaces. Eigenvalues and eigenvectors of a linear transformation

$\S 11$. The adjoint of a linear transformation

$\S 12$. Self-adjoint (Hermitian) transformations. Simultaneous reduction of a pair of quadratic forms to a sum of squares

$\S 13$. Unitary transformations

$\S 14$. Commutative linear transformations. Normal transformations

$\S 15$. Decomposition of a linear transformation into a product of a unitary and self-adjoint transformation

$\S 16$. Linear transformations on a real Euclidean space

$\S 17$. Extremal properties of eigenvalues

$\text {III}$. The Canonical Form of an Arbitrary Linear Transformation

$\S 18$. The canonical form of a linear transformation

$\S 19$. Reduction to canonical form

$\S 20$. Elementary divisors

$\S 21$. Polynomial matrices

$\text {IV}$. Introduction to Tensors

$\S 22$. The dual space

$\S 23$. Tensors

Next

Further Editions

• 1948: I.M. Gel'fand: Lektsii po Lineinoi Algebre
• 1950: I.M. Gel'fand: Lektsii po Lineinoi Algebre (2nd ed.)

Source work progress

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