Matrix Decompositions Involving the Schur Complement
Copyright policy )Matrix Decompositions Involving the Schur Complement
Necessary and sufficient conditions are given for the rank of a sum of matrices over an arbitrary field to equal the sum of the ranks of the matrices. Several decompositions are given of a partitioned matrix into a sum of matrices. These provide a unified treatment of some classical results and some recent results on the ranks and generalized inverses of partitioned matrices, and lead to an abstract characterization of a concept related to the previously studied Schur complement.
Vector spaces, linear dependence, rank, lineability, Matrix equations and identities, Theory of matrix inversion and generalized inverses
Vector spaces, linear dependence, rank, lineability, Matrix equations and identities, Theory of matrix inversion and generalized inverses
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