Motivated by state space realizations of transfer functions from system theory, a number of operations on Schur complements are introduced and studied. These operations are equivalence, extension, multiplication, inversion, and factorization. Together they form an algebraic framework which is of independent interest, and also useful in solving problems in analysis.

Equivalence, Extension, Factorization, Realization, Schur complement, Transfer function,
Linear Algebra and Its Applications
Erasmus School of Economics

Bart, H, Gohberg, I, Kaashoek, J.F, & Ran, L. (2005). Schur complements and state space realizations. In Linear Algebra and Its Applications (Vol. 399, pp. 203–224). doi:10.1016/j.laa.2004.10.027