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Full Description
Matrix theory is the lingua franca of everyone who deals with dynamically evolving systems, and familiarity with efficient matrix computations is an essential part of the modern curriculum in dynamical systems and associated computation. This is a master's-level textbook on dynamical systems and computational matrix algebra. It is based on the remarkable identity of these two disciplines in the context of linear, time-variant, discrete-time systems and their algebraic equivalent, quasi-separable systems. The authors' approach provides a single, transparent framework that yields simple derivations of basic notions, as well as new and fundamental results such as constrained model reduction, matrix interpolation theory and scattering theory. This book outlines all the fundamental concepts that allow readers to develop the resulting recursive computational schemes needed to solve practical problems. An ideal treatment for graduate students and academics in electrical and computer engineering, computer science and applied mathematics.
Contents
Part I. Lectures on Basics, with Examples: 1. A first example: optimal quadratic control; 2. Dynamical systems; 3. LTV (quasi-separable) systems; 4. System identification; 5. State equivalence, state reduction; 6. Elementary operations; 7. Inner operators and external factorizations; 8. Inner-outer factorization; 9. The Kalman filter as an application; 10. Polynomial representations; 11. Quasi-separable Moore-Penrose inversion; Part II. Further Contributions to Matrix Theory: 12. LU (spectral) factorization; 13. Matrix Schur interpolation; 14. The scattering picture; 15. Constrained interpolation; 16. Constrained model reduction; 17. Isometric embedding for causal contractions; Appendix. Data model and implementations; References; Index.
