Abstract
Partitioned matrices satisfying certain null space properties for all leading principal submatrices are shown to be equivalent to a sequence of generalized Schur complements satisfying the same null space properties with respect to their (1, 1) entry. It is shown that a matrix with these null space properties has nonsingular principal submatrices of all orders less than or equal to its rank. Also, a theorem of Carlson, Haynsworth, and Markham concerning the quotient property for Schur complements is extended.
Published Version
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