Relationship between the Karhunen- Loéve transform and the Courant - Fischer theorem (Corresp.)

It is shown that the Karhunen-Loève transform problem can be formulated as a matrix approximation problem with Hilbert-Schmidt error norm. On the other hand, the Courant-Fischer minimax theorem provides a characterization for the best matrix approximation when the spectral norm is used. It appears t...

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Veröffentlicht in:	IEEE transactions on information theory 1984-07, Vol.30 (4), p.662-664
Hauptverfasser:	Delsarte, P., Kamp, Y.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Exact sciences and technology Information, signal and communications theory Telecommunications and information theory
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Beschreibung
Zusammenfassung:	It is shown that the Karhunen-Loève transform problem can be formulated as a matrix approximation problem with Hilbert-Schmidt error norm. On the other hand, the Courant-Fischer minimax theorem provides a characterization for the best matrix approximation when the spectral norm is used. It appears that the optimality conditions of the Karhunen-Loève problem lead to the selection of a particular solution among the set of solutions to the Courant-Fischer problem.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.1984.1056938