The Theory of Matrices: With Applications

 Maxtrix Algebra. Determinants, Inverse Matrices, and Rank. Linear, Euclidean, and Unitary Spaces. Linear Transformations and Matrices. Linear Transformations in Unitary Spaces and Simple Matrices. The Jordan Canonical Form: A Geometric Approach. Matrix Polynomials and Normal Forms. The Variational Method. Functions of Matrices. Norms and Bounds for Eigenvalues. Perturbation Theory. Linear Matrix Equations and Generalized Inverses. Stability Problems. Matrix Polynomials. Nonnegative Matrices. Appendix 1. A Survey of Scalar Polynomials. Appendix 2. Some Theorems and Notions from Analysis. Appendix 3. Suggestions for Further Reading. Index.