Texts and Readings in Mathematics

The vector space approach to the treatment of linear algebra is useful for geometric intuition leading to transparent proofs; it's also useful for generalization to infinite-dimensional spaces. The Indian School, led by Professors C. R. Rao and S. K. Mitra, successfully employed this approach. This book follows their approach and systematically develops the elementary parts of matrix theory, exploiting the properties of row and column spaces of matrices.

Developments in linear algebra during the past few decades have brought into focus several techniques not included in basic texts, such as rank-factorization, generalized inverses, and singular value decomposition. These techniques are actually simple enough to be taught at the advanced undergraduate level. When properly used, they provide a better understanding of the topic and give simpler proofs, making the subject more accessible to students.

This book explains these techniques. It is intended as a textbook for the advanced student of mathematics and/or statistics. It will also be useful for students of physics, computer science, engineering, operations research, and research scientists.
1.Preliminaries
2.Vector spaces
3.Algebra of matrices
4.Rank and inverse
5.Elementary operations and reduced forms
6.Linear equations
7.Determinants
8.Inner product and orthogonality
9.Eigenvalues
10.Quadratic forms
References
More hints and solutions
List of symbols
Index