ELA, Volume 8, pp. 115-127, August 2001, abstract.

How to establish universal block-matrix factorizations
                
Yongge Tian and George P. H. Styan

A general method is presented for establishing universal 
factorization equalities for 2x2 and 4x4 block matrices. 
As applications, some universal factorization equalities for 
matrices over four-dimensional algebras are established, 
in particular, over the Hamiltonian quaternion algebra.