Polar decompositions X=UA of real and complex matrices X with respect to the scalar product generated by a given indefinite nonsingular matrix H are studied in the following special cases: (1) X is an H-contraction, (2) X is an H-plus matrix, (3) H has only one positive eigenvalue, and (4) U belongs to the connected component of the identity in the group of H-unitary matrices. Applications to linear optics are presented.
Polar decompositions in finite dimensional indefinite scalar product spaces: Special cases and applications
VAN DER MEE, CORNELIS VICTOR MARIA;
1996-01-01
Abstract
Polar decompositions X=UA of real and complex matrices X with respect to the scalar product generated by a given indefinite nonsingular matrix H are studied in the following special cases: (1) X is an H-contraction, (2) X is an H-plus matrix, (3) H has only one positive eigenvalue, and (4) U belongs to the connected component of the identity in the group of H-unitary matrices. Applications to linear optics are presented.
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