Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Lectures on Basics with Examples
- 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
17 - Isometric Embedding for Causal Contractions
from Part II - Further Contributions to Matrix Theory
Published online by Cambridge University Press: 24 October 2024
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Part I Lectures on Basics with Examples
- 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
Summary
The final chapter completes the scattering theory with an elementary approach to inner embedding of a contractive, quasi-separable causal system (in engineering terms: the embedding of a lossy or passive system in a lossless system, often called Darlington synthesis). Such an embedding is always possible in the finitely indexed case but does not generalize to infinitely indexed matrices. (This last issue requires more advanced mathematical methods and lies beyond the subject matter of the book.)
- Type
- Chapter
- Information
- Time-Variant and Quasi-separable SystemsMatrix Theory, Recursions and Computations, pp. 277 - 291Publisher: Cambridge University PressPrint publication year: 2024