A Schur complement inequality for certain P-matrices Original Research Article

Suppose A and B are n × n matrices over the complex field. An inequality is derived that relates the Schur complement of the Hadamard product of A and B and the Hadamard product of Schur complements of A and B for positive definite matrices. Then an analog is given for the class of tridiagonal totally nonnegative matrices. A similar result is given for classes of Z-matrices where the Hadamard product is replaced by the Fan product.