Symmetrizable Generalized Inverses of Symmetrizable Matrices

The matrix A is said to be symmetri zable by V when V is positive definite and AV is hermitian. Several le mmas regard ing symmetrizability are given. For three classes of generalized inverses it is s hown that if A is s mmetrizable by V the re exists a generali zed inverse in each class which is sy mmetrizable by V. The Moore·Penrose inverse (or pseudo-inverse) of a matrix symmetrizable by V is also symmetrizable by V if and only if the matrix and the pseudo-inverse com mute.