Inversion and canonization of block matrices

The paper is concerned with the problem of inverting block matrices to which the well-known Frobenius–Schur formulas are not applicable. These can be square matrices with four noninvertible square or rectangular blocks as well as square or rectangular matrices with two blocks. With regard to rectangular matrices, the results obtained are a further step in the development of the canonization method, which is used for solving arbitrary matrix equations.