Linear Algebra

1. Front Matter

   Pages i-xiii

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2. Preliminaries

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 1-13

3. Vector spaces

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 14-66

4. Algebra of matrices

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 67-107

5. Rank and inverse

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 108-156

6. Elementary operations and reduced forms

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 157-184

7. Linear equations

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 185-217

8. Determinants

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 218-247

9. Inner product and orthogonality

   • A. Ramachandra Rao, P. Bhimasankaram

   Pages 248-279

10. Eigenvalues

    • A. Ramachandra Rao, P. Bhimasankaram

    Pages 280-327

11. Quadratic forms

    • A. Ramachandra Rao, P. Bhimasankaram

    Pages 328-366

12. Back Matter

    Pages 367-414

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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 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.

• Indian Statistical Institute, Calcutta, India

  A. Ramachandra Rao

• Indian Statistical Institute, Hyderabah, India

  P. Bhimasankaram