[1] [2000] [1977] [Gantmakher, F.R.] [Hirsch, K.A. tran.] The Theory of Matrices, Volume 1, Reprint

Volume 1 only. Owner name and date written on first end page. Pages are clean and binding is tight. V.1. Matrices And Operations Of Matrices -- The Algorithm Of Gauss And Some Of Its Applications -- Linear Operations In An N-dimensional Vector Space -- The Characteristic Polynomial And The Minimal Polynomial Of A Matrix -- Functions Of Matrices -- Equialent Transformations Of Polynomial Matrices. Analytic Theory Of Elementary Divisors -- The Structure Of A Linear Operation In An N-dimensional Space -- Matrix Equations -- Linear Operators In A Unitary Space -- Quadratic And Hermitian Forms -- V.2. Complex Symmetric, Skew-symmetric, And Orthogonal Matrices -- Singular Pencils Of Matrices -- Matrices With Non-negative Elements -- Applications Of The Theory Of Matrices To The Investigation Of Systems Of Linear Differential Equations -- The Problem Of Routh-hurwitz And Related Questions. By F.r. Gantmacher. [translation By K.a. Hirsch] Translation Of: Teorii︠a︡ Matrit︠s︡. Includes Bibliographies. Includes Bibliographical References. This treatise, by one of Russia's leading mathematicians, gives in easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, electrical engineering, etc. The individual chapters have been kept as far as possible independent of each other, so that the reader acquainted with the contents of Chapter 1 can proceed immediately to the chapters of special interest. Much of the material has been available until now only in the periodical literature This treatise, by one of Russia's leading mathematicians, gives in easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, electrical engineering, etc. The individual chapters have been kept as far as possible independent of each other, so that the reader acquainted with the contents of Chapter 1 can proceed immediately to the chapters of special interest. This is an excellent textbook. —Zentralblatt MATH In Volume I, Chapter IX, in connection with the study of linear operators in a euclidean space, we investigated real symmetric, skew-symmetric, and orthogonal matrices, i.e., real square matrices characterized by the relations. Presents an account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, and electrical engineering.