Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 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
- Appendix: Data Model and Implementations
- References
- Index
11 - Quasi-separable Moore−Penrose Inversion
from Part I - Lectures on Basics with Examples
Published online by Cambridge University Press: 24 October 2024
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 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
- Appendix: Data Model and Implementations
- References
- Index
Summary
This chapter considers the Moore–Penrose inversion of full matrices with quasi-separable specifications, that is, matrices that decompose into the sum of a block-lower triangular and a block-upper triangular matrix, whereby each has a state-space realization given. We show that the Moore–Penrose inverse of such a system has, again, a quasi-separable specification of the same order of complexity as the original and show how this representation can be recursively computed with three intertwined recursions. The procedure is illustrated on a 4 ? 4 (block) example.
- Type
- Chapter
- Information
- Time-Variant and Quasi-separable SystemsMatrix Theory, Recursions and Computations, pp. 169 - 182Publisher: Cambridge University PressPrint publication year: 2024