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## 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.