2013 Reprint of 1961 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. 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. Georgi Shilov was a Soviet mathematician and expert in the field of functional analysis, who contributed...