Description
Hindustan Book Agency Linear Algebra and Linear Models 2012 Edition by 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.
This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.
Table of Contents
Vector Spaces and Subspaces
Rank, Inner Product and Nonsingularity
Eigenvalues and Positive Definite Matrices
Generalized Inverses
Inequalities for Eigenvalues and Singular Values
Rank Additivity and Matrix Partial Orders
Linear Estimation
Tests of Linear Hypotheses
Linear Mixed Models
Miscellaneous Topics
Additional Exercises on Rank
Hints and Solutions to Selected Exercises
Notes
References
Index