Title: The theory of matrices :
Authors: Lancaster, Peter,; Tismenetsky, Miron.
Date: 1985
Publisher: Academic Press,
Physical description: xv, 570 pages ; 24 cm.
Language: English
LC classification: Q
Abstract: "In this book the authors try to bridge the gap between the treatments of matrix theory and linear algebra to be found in current textbooks and the mastery of these topics required to use and apply our subject matter in several important areas of application, as well as in mathematics itself. At the same time we present a treatment that is as self-contained as is reasonable possible, beginning with the most fundamental ideas and definitions. In order to accomplish this double purpose, the first few chapters include a complete treatment of material to be found in standard courses on matrices and linear algebra. This part includes development of a computational algebraic development (in the spirit of the first edition) and also development of the abstract methods of finite-dimensional linear spaces. Indeed, a balance is maintained through the book between the two powerful techniques of matrix algebra and the theory of linear spaces and transformations."--1st paragraph of preface.
Contents: Matrix algebra -- Determinants, inverse matrices, and rank -- Linear, Euclidean and unitary spaces -- Linear transformations and matrices -- Linear transformations in unitary spaces and simple matrices -- The Jordan canonical form: a geometric approach -- Matrix polynomials and normal forms -- The variational method -- Functions of matrices -- Norms and bounds for eigenvalues -- Perturbation theory -- Linear matrix equations and generalized inverses -- Stability problems -- Matrix polynomials -- Nonnegative matrices -- Appendix 1: A survey of scalar polynomials -- Appendix 2: Some theorems and notions from analysis -- Appendix 3: Suggestions for further reading.
Notes: Includes index.
Subject headings (LCSH): Matrices.