The theory of matrices. Vol. 2. Transl. from the Russian by K. A. Hirsch. Reprint of the 1959 translation.

*(English)*Zbl 0927.15002
Providence, RI: AMS Chelsea Publishing. ix, 276 p. (1998).

[For a review of the first Russian edition (1953) see Zbl 0050.24804. For the first part of this edition see the preceding review Zbl 0927.15001]

This is an excellent and unusual textbook on the application of the theory of matrices. This second part consists of the following five chapters: XI: Complex symmetric, skew-symmetric, and orthogonal matrices; XII. Singular pencils of matrices; XIII: Matrices with non-negative elements; XIV: Applications of the theory of matrices to the investigations of systems of linear differential equations; XV: The problem of Routh-Hurwitz and related questions.

In spite of intensive developments in the theory of matrices and the appearance of other significant books, both general and specialized, in the last four decades, this monograph has retained its leading role. This textual matter includes many chapters of interest to applied mathematicians.

This is an excellent and unusual textbook on the application of the theory of matrices. This second part consists of the following five chapters: XI: Complex symmetric, skew-symmetric, and orthogonal matrices; XII. Singular pencils of matrices; XIII: Matrices with non-negative elements; XIV: Applications of the theory of matrices to the investigations of systems of linear differential equations; XV: The problem of Routh-Hurwitz and related questions.

In spite of intensive developments in the theory of matrices and the appearance of other significant books, both general and specialized, in the last four decades, this monograph has retained its leading role. This textual matter includes many chapters of interest to applied mathematicians.

Reviewer: T.Nôno (Hiroshima)

##### MSC:

15-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra |

34A30 | Linear ordinary differential equations and systems, general |

34Dxx | Stability theory for ordinary differential equations |

01A75 | Collected or selected works; reprintings or translations of classics |