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Linear algebra. 3rd ed. (English) Zbl 0618.15001

Undergraduate Texts in Mathematics. New York etc.: Springer-Verlag. IX, 285 p.; DM 78.00 (1987).
The book is intended as a text for a second course in linear algebra. The first six chapters cover most of the material contained in the author’s Introduction to Linear Algebra (First edition 1970; Zbl 0216.06001, second edition 1986; Zbl 0577.15001). The presentation is more abstract, however, and proceeds appreciably faster. The author emphasizes that this is to make the book selfcontained but the text is not intended as a substitute for the introductory one. Linear spaces are considered over an arbitrary subfield of the field of complex numbers. As opposed to the introductory text there is a complete theory of determinants, a broader discussion of Hermitian and unitary operators, more about eigenvalue problems. Two chapters are devoted to polynomial matrices and the Jordan normal form. A brief treatment of convexity culminating in the Krein- Milman theorem concludes the book.
Reviewer: V.Pták

MSC:

15-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
65F05 Direct numerical methods for linear systems and matrix inversion