×

A note on the hyperbolic singular value decomposition. (English) Zbl 0933.15016

Summary: A procedure is presented for constructing the hyperbolic singular value decomposition of a matrix \(A\) with respect to a signature matrix \(\Phi\). When the rank of \(A\) is less than the rank of \(A^H\Phi A\), the decomposition preserves the structure of the isotropic subspace of the column space of \(A\).

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15A23 Factorization of matrices
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Onn, R.; Steinhardt, A. O.; Bojanczyk, A. W., The hyperbolic singular value decomposition and applications, (IEEE Trans. Signal Proc., 39 (1991)), 1575-1588
[2] Rader, C. M.; Steinhardt, A. O., Hyperbolic Householder transformations, (IEEE Trans. Acoust., Speech, Signal Proc., 34 (1986)), 1589-1602 · Zbl 0629.93063
[3] Rader, C. M.; Steinhardt, A. O., Hyperbolic Householder transforms, SIAM J. Matrix Anal. Appl., 9, 269-290 (1988) · Zbl 0647.65027
[4] Bojanczyk, A. W.; Onn, R.; Steinhardt, A. O., Existence of the hyperbolic singular value decomposition, Linear Algebra Appl., 185, 21-30 (1993) · Zbl 0778.15005
[5] Zha, H., A note on the existence of the hyperbolic singular value decomposition, Linear Algebra Appl., 240, 199-205 (1996) · Zbl 0923.15007
[6] Haykin, S., Adaptive Filter Theory (1996), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[7] Hassibi, B.; Sayed, A. H.; Kailath, T., Linear estimation in Krein spaces — Part I: Theory, IEEE Trans. Automat. Contr., 41, 18-33 (1996) · Zbl 0862.93055
[8] Hassibi, B.; Sayed, A. H.; Kailath, T., Linear estimation in Krein spaces — Part II: Applications, IEEE Trans. Automat. Contr., 41, 34-49 (1996) · Zbl 0862.93056
[9] Paige, C. C., The general linear model and the generalized singular value decomposition, Linear Algebra Appl., 70, 269-284 (1985) · Zbl 0587.62135
[10] Levy, B. C.; Benveniste, A.; Nikoukhah, R., High-level primitives for recursive maximum likelihood estimation, IEEE Trans. Automat. Contr., 41, 1125-1145 (1996) · Zbl 0860.93030
[11] B.C. Levy, R. Nikoukhah, A. Benveniste, A Krein-space estimation view of LEQG control (in preparation).; B.C. Levy, R. Nikoukhah, A. Benveniste, A Krein-space estimation view of LEQG control (in preparation).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.