Nullities of submatrices of the Moore-Penrose inverse
If \(A=(A_{ij})\) and its Moore-Penrose inverse \(A^{\dag}=(B_{ij})\) are partitioned matrices with compatible splittings, then the paper gives lower and upper bounds on the difference of nullities \(\eta (B_{22})- \eta (A_{11})\). The bounds are expressed in terms of the number of rows and columns of A, its rank, and the nullities of certain blocks of the corresponding projection matrices \(AA^{\dag}\) and \(A^{\dag}A\). Proofs use the singular value decomposition theorem.
scientific article; zbMATH DE number 4017095