This exploration of quadratic forms over rational numbers and rational integers offers an elementary introduction that includes recent developments. Topics include the theory of quadratic forms over local fields, forms with integral coefficients, genera and spinor genera, reduction theory for definite forms, and Gauss' composition theory. 1968 edition. Reprint of the Academic Press, London and New York, 1968 edition.
Linear Algebra by Georgi E. Shilov 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, and more.
Lectures on Linear Algebra by I. M. Gel’fand Prominent Russian mathematician's concise, well-written exposition considers: n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, introduction to tensors, more. 1961 edition.
