The theory of matrices. Vol. 1. Transl. from the Russian by K. A. Hirsch. Reprint of the 1959 translation. (English) Zbl 0927.15001

Gantmacher, F. R.

Providence, RI: AMS Chelsea Publishing. x, 374 p. (1998).

[For a review of the first Russian edition (1953) see Zbl 0050.24804.]
This is an excellent textbook consisting of the following usual ten chapters: I: Matrices and operations on matrices; II: The algorithm of Gauss and some of its applications; III: Linear operators in an \(n\)-dimensional vector space; IV: The characteristic polynomial and the minimal polynomial of a matrix; V: Functions of matrices; IV: Equivalent transformations of polynomial matrices. Analytic theory of elementary divisors; VII: The structure of linear operators in an \(n\)-dimensional space; VIII: Matrix equations; IX: Linear operators in a unitary space; X: Quadratic and Hermitian forms.

Reviewer: T.Nôno (Hiroshima)

MSC:

15-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
01A75	Collected or selected works; reprintings or translations of classics
65F05	Direct numerical methods for linear systems and matrix inversion

Keywords:

theory of matrices; Gauss algorithm; reprint of classics; linear operators; matrix equations; quadratic and Hermitian forms; textbook; vector space; characteristic polynomial; minimal polynomial; polynomial matrices; elementary divisors

Citations:

Zbl 0050.24804