Matrix Algebra

Contents: Preface. Matrix (mathematics). 1. Matrix algebra: introduction. 2. Multiplication of matrices. 3. Algebraic properties of matrix operations. 4. Invertible matrices. 5. Special matrices: triangular, symmetric, diagonal. 6. Elementary operations for matrices. 7. Matrix exponential. 8. Complex numbers as matrices. 9. Markov chains. 10. System of equations: an introduction. 11. System of linear equations: Gaussian Elimination. 12. System of equations in two variables. 13. System of equations in three variables. 14. Application of determinant to systems: Cramer\'s rule. 15. Introduction to determinants. 16. Determinants of matrices of higher order. 17. Determinant and inverse of matrices. 18. Application of determinant to systems: Cramer\'s rule. 19. Eigenvalues and Eigenvectors: an introduction. 20. Computation of Eigenvalues. 21. The case of complex Eigenvalues. 22. Diagonalization.

"Fully rigorous treatment starts with basics and progresses to sweepout process for obtaining complete solution of any given system of linear equations and role of matrix algebra in presentation of useful geometric ideas, techniques, and terminology. Also, commonly used properties of determinants, linear operators and linear transformations of coordinates." (jacket)