Introductory treatment offers a clear exposition of algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. Numerous examples illustrate many different fields, and problems include hints or answers. 1961 edition.

1. Determinants
2. Linear Spaces
3. Systems of Linear Equations
4. Linear Functions of a Vector Argument
5. Coordinate Transformations
6. Bilinear and Quadratic Forms
7. Euclidean Spaces
8. Orthogonalization and the Measurement of Volume
9. Invariant Subspaces and Eigenvectors
10. Quadratic Forms in a Euclidean Space
11. Quadric Surfaces
12. Infinite-Dimensional Euclidean Spaces
Bibliography
Index

Soviet mathematician Georgi E. Shilov (1917-75) was a longtime Professor of Mathematics at Moscow State University and the author of several other successful Dover reprints.