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\iteman{io-port 04002273}
\itemau{Lang, Serge}
\itemti{Linear algebra. 3rd ed.}
\itemso{Undergraduate Texts in Mathematics. New York etc.: Springer-Verlag. IX, 285 p.; DM 78.00 (1987).}
\itemab
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.
\itemrv{V.Pt\'ak}
\itemcc{}
\itemut{textbook; Gauss elimination; linear spaces; rank; determinant; exercises; Hermitian and unitary operators; eigenvalue problems; polynomial matrices; Jordan normal form; convexity; Krein-Milman theorem}
\itemli{}
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