Crawford's A matrix in the theory of molecular vibrations is, in a sense, the inverse of Wilson's B matrix, but is not unique because B is rectangular. We consider the general form of A and then use the Eckart conditions to obtain the solution A = M(-1)B(T)G(-1), which has been widely used. Although the internal-coordinate harmonic force constants f = A(T)F(X)A, where F(X) are the Cartesian force constants, are superficially isotope-dependent, we show that this dependence vanishes. More generally, solutions of the form A = WB(T)(BWB(T))(-1), where W is an arbitrary nonsingular square matrix, are shown to give an f matrix that is independent of W. Copyright 2001 Academic Press.