Matrix Theory

The aim of this text is to present fundamental ideas, results, and techniques concisely, mainly in matrix theory with some in linear algebra. The book contains ten chapters covering various topics ranging from rank, similarity, and special matrices, to Schur complements, matrix normality, and majorization. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. Major changes in this third edition include:

• expansion of topics such as eigenvalue continuity, matrix functions, nonnegative matrices, matrix norms, and majorization
• inclusion of more than 200 examples and more than 1500 exercises
• emphasis on basic techniques and skills for partitioned matrices through which a variety of matrix results and matrix inequalities are shown
• showcase of many majorization-type inequalities for diagonal entries, eigenvalues, and singular values of matrices.

This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for advanced undergraduate or graduate students. Prerequisites include a solid background in elementary linear algebra and calculus. The text can also serve as a reference for researchers in algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other scientific areas.

From reviews of the second edition:

The author has made a valuable contribution to the textbook literature on matrix theory, and his w

Preface to the Third Edition. - Frequently Used Notation and Terminology. - Frequently Used Terms. - 1. Elementary Linear Algebra Review. - 2. Partitioned Matrices, Rank, and Eigenvalues. - 3. Matrix Polynomials and Canonical Forms. - 4. Numerical Ranges, Norms, and Special Products of Matrices. - 5. Special Types of Matrices. - 6. Unitary Matrices and Contractions. - 7. Positive Semidefinite Matrices. - 8. Hermitian Matrices. - 9. Normal Matrices. - 10. Majorization and Matrix Inequalities. - References. - Notation. - Index.