Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Here's a sample of other books in this Dover category
Rational Quadratic Forms by J. W. S. Cassels Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.
Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form by I. M. Glazman, Ju. I. Ljubic, G. P. Barker, G. Kuerti A sequence of 2,400 propositions and problems features only hints.Suitable for advanced undergraduates and graduate students, this unique approach encourages students to work out their own proofs. 1974 edition.
Linear Algebra and Projective Geometry by Reinhold Baer Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.
Linear Algebra and Geometry: A Second Course by Irving Kaplansky The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. This volume features examples, exercises, and proofs. 1974 edition.
Modern Algebra by Seth Warner Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
