BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-89-06
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: On the structure and geometry of the product singular value
               decomposition
        TYPE:: Manuscript
      AUTHOR:: De Moor, Bart L. R.
        DATE:: May 1989
       PAGES:: 54
    ABSTRACT:: The product singular value decomposition is a factorization
               of two matrices, which can be considered as a generalization
               of the ordinary singular value decomposition, at the same
               level of generality as the quotient (generalized) singular
               value decomposition.

               A constructive proof of the product singular value
               decomposition is provided, which exploits the close relation
               with a symmetric eigenvalue problem. Several interesting
               properties are established.

               The structure and the non-uniqueness properties of the so
               called contragredient transformation, which appears as one of
               the factors in the product singular value decomposition, are
               investigated in detail. Finally, a geometrical interpretation
               of the structure is provided in terms of principal angles
               between subspaces.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-89-06