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On Calculation of Pseudoinverse Square Matrix Based on Inversion

Authors: Zubov N.E., Mikrin E.A., Ryabchenko V.N. Published: 08.06.2018
Published in issue: #3(78)/2018  
DOI: 10.18698/1812-3368-2018-3-24-31

 
Category: Mathematics and Mechanics | Chapter: Differential Equations and Mathematical Physics  
Keywords: inverse matrix, pseudoinverse matrix, pseudoinverse matrix calculation formulae

The paper focuses on the new formulae obtained for calculation of the Moore --- Penrose pseudoinverse matrix for a given quadratic matrix. The formulae are based on conversion as a sum of the given matrix and the exterior product of its left and right zero divisors by means of the inverse matrix. Such conversion allows us to use the standard calculation algorithms for pseudoinversion, improve equation conditionality in the case of badly scaled matrix pseudoinversion and complete pseudoinversion of symbolic matrixes. The paper exemplifies inversion of a low rank symbolic matrix. Finally, the set of corollaries from the theorems defining the pseudoinverse matrix calculation formulae is considered and a procedure of improving calculation accuracy of the pseudoinverse matrix is described

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