FURTHER GEOMETRIC RESTRICTIONS ON JORDAN STRUCTURE IN MATRIX FACTORIZATION

Charles R. Johnson, Drew Lewis, YuLin Zhang
2012 Asian-European Journal of Mathematics  
It is known that a nonsingular, nonscalar, n-by-n complex matrix A may be factored as A = BC, in which the spectra of B and C are arbitrary, subject to det(A) = det(B)det(C). Furthermore, it is also known that B and C can be taken to be nonderogatory. Additionally it has been shown that when two matrices have eigenvalues of high geometric multiplicity, this restricts the possible Jordan structure of the third. We demonstrate a previously unknown restriction on the Jordan structures of B and C.
more » ... urthermore, we show that this generalized geometric multiplicity restriction implies the already known geometric multiplicity restriction, show that the new condition is more restrictive, is not sufficient in general but is sufficient in a situation that we identify.
doi:10.1142/s1793557112500180 fatcat:uccsegqyl5butal6fce26mo5gy