## Texts and Readings in Mathematics

Linear Algebra and Linear Models (3/E)

R. B. Bapat

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. Emphasis is given to the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included.

For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters. It will serve as a first course on linear algebra that is especially suitable for students of statistics or those looking for a matrix theoretic approach to the subject. Other key features include:

- coverage of topics such as rank additivity, inequalities for eigenvalues and singular values
- a new chapter on linear mixed models
- over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices

Contents

1. Vector Spaces and Subspaces 2. Rank, Inner Product and Nonsingularity

3. Eigenvalues and Positive Definite Matrices

4. Generalized Inverses

5. Inequalities for Eigenvalues and Singular Values

6. Rank Additivity and Matrix Partial Orders

7. Linear Estimation

8. Tests of Linear Hypotheses

9. Linear Mixed Models

10. Miscellaneous Topics

11. Additional Exercises on Rank

12. Hints and Solutions to Selected Exercises

13. Notes

References

Index

Linear Algebra and Linear Models (3/E)

2012, 9789380250281, 182 pages, paper cover, Rs. 350.00

2012, 9789380250281, 182 pages, paper cover, Rs. 350.00