Generalized inverses with proportional minors

AbstractLet A, H be matrices of rank r and of order m×n and n×m respectively over an integral domain. It is shown that A admits a g-inverse whose r×r minors are propotional to the corresponding minors of H if and only if the trace of the rth compound of AH is invertible. We also obtain a determinantal formula for such a g-inverse when it exists. The results generalize earlier work on the existence of the Moore-Penrose and group inverses