  We show that any nonsingular (real or complex) square matrix can be
factorized into a product of at most three normal matrices, one of which is
unitary, another selfadjoint with eigenvalues in the open right half-plane, and
the third one is normal involutory with a neutral negative eigenspace (we call
the latter matrices normal neutral involutory). Here the words normal, unitary,
selfadjoint and neutral are understood with respect to an indefinite inner
product.
