Equivalence of partitioned matrices
Robert B. Feinberg · Journal of Research of the National Bureau of Standards Section B Mathematical Sciences · 1976
It is s ho wn that if M = [~ ~] is a partition e d matrix over a prin c ipal id ea l domain I? s uc h th a t th e matri ces A and B a re both s qu are, th e n Mi s e quiva le nt to A + B (=) th e matri c e qu a ti o n T= AY + XB is so lvab le.Th e res ult is ge ner a lized to trea t th e c a se wh e n Mil MI2 Mil M = o o o M" wh e re eac h M u is s quare .