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17 - Isometric Embedding for Causal Contractions

from Part II - Further Contributions to Matrix Theory

Published online by Cambridge University Press:  24 October 2024

Patrick Dewilde
Affiliation:
Technische Universität München
Klaus Diepold
Affiliation:
Technische Universität München
Alle-Jan Van der Veen
Affiliation:
Technische Universiteit Delft, The Netherlands
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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.)

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Time-Variant and Quasi-separable Systems
Matrix Theory, Recursions and Computations
, pp. 277 - 291
Publisher: Cambridge University Press
Print publication year: 2024

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