Georgi E. Shilov

This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers. 1961 edition.

In this volume in his exceptional series of translations of Russian mathematical texts, Richard Silverman has taken Shilov's course in linear algebra and has made it even more accessible and more useful for English language readers. Georgi E. Shilov, Professor of Mathematics at the Moscow State University, 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 algebras and their representations, with an appendix on categories of finite-dimensional spaces. The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back. Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom. Reprint of the original 1971 edition.

Starting with the useful concept of an elementary integral defined (axiomatically) on a family of elementary functions, this treatment examines the general theory of the integral, Lebesque integral in "n "space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." -- "Sci-Tech Book News."" "1966 edition.