Georgi E. Shilov. Translated by Richard A. Silverman

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

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.