Restricted Singular Value Decomposition of Matrix Triplets.
Please always quote using this URN: urn:nbn:de:0297-zib-205
- In this paper we introduce the concept of restricted singular values (RSV's) of matrix triplets. A theorem concerning the RSV's of a general matrix triplet $ (A,B,C) $, where $ A \in C^{m\times n} $, $B\in C^{m\times p} $ and $ C\in C^{q\times n} $, which is called restricted singular value decomposition (RSVD) of matrix triplets, is derived. This result generalizes the wellknown SVD, GSVD and the recently proposed product induced SVD (PSVD). Connection of RSV's with the problem of determination of matrix rank under restricted perturbation is also discussed. {\bf Keywords:} Matrix rank, singular values, generalized singular values, product induced singular values, restricted singular values, matrix decompositions.
| Author: | Hongyuan Zha |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | Matrix rank; generalized singular values; matrix decompositions; product induced singular values; restricted singular values; singular values |
| MSC-Classification: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A09 Matrix inversion, generalized inverses |
| 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A12 Conditioning of matrices [See also 65F35] | |
| 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A23 Factorization of matrices | |
| 65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F20 Overdetermined systems, pseudoinverses | |
| Date of first Publication: | 1989/03/22 |
| Series (Serial Number): | ZIB-Report (SC-89-02) |
| ZIB-Reportnumber: | SC-89-02 |
| Published in: | Appeared in: SIAM J. Matrix Analysis and Applications 12 (1991) pp. 172-194 |
