A note on the product of two matrices of index one
Johanns de Andrade Bezerra · Linear and Multilinear Algebra · 2016
In this paper, we show some necessary and/or sufficient conditions so that AB and/or BA are core matrices, whenever A and B are core complex matrices (a matrix A is a core matrix, that is a matrix of index one, if ). More specifically, we also analyse some similar situations where A, B, AB and/or BA are diagonalizable matrices or EP matrices. Moreover, we provide, as an application, two results concerning the reverse order law for the Moore–Penrose inverse of the product of two matrices.