On Calculating a Pseudoinverse Matrix. General Case

The study proposes a universal approach for analytical calculation of a pseudoinverse matrix for both rectangular, and square matrices. According to this approach, we obtained a formula that, in fact, relates the operation of inversion of a nondegenerate block matrix composed of a given matrix and its left and right zero divisors of maximal rank, to a pseudoinversion of this matrix. The paper gives the theorem and its proof. Within the research we investigate the main properties of the chosen formula and formulate the corollaries that have practical value and simplify the computation of the pseudoinverse matrix. Moreover, we consider semiorthogonal matrix zero divisors and matrices that do not have this property. The examples given are illustrative and are related to inversion of matrix of both square, and rectangular types of low rank

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