On generalized Schur complement of matrices and its applications to real and integer matrix factorizations

Document Type : Research Article


Department of mathematics, University of Qom, Qom, Iran


We provide a general finite iterative approach for constructing factorizations of a matrix $A$   under a common framework of a general decomposition $A=BC$  based on the generalized Schur complement. The approach  applies  a zeroing process using  two index sets. Different choices of the index sets  lead to different real and integer matrix  factorizations.    We also provide the  conditions under which this approach is well-defined.