PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 45(59), pp. 57--63 (1989)
ON SOME GENERALIZED INVERSES OF MATRICES AND SOME LINEAR MATRIX EQUATIONS
Jovan D. Ke\v cki\'cFarmaceutski fakultet, Beograd, Yugoslavia
Abstract: We point a generalized inverse $A_G$ of a singular square complex matrix $A$, with the property that the general solution of the equation $A^nx=0$ (and many other equations) can be expressed by means of $A_G$ for all positive integers $n$. This inverse is a solution of the system (5), also satisfied by the strong spectral inverse of Greville. Applications to various matrix equations and to linear algebraic systems are given.
Classification (MSC2000): 15A09, 15A24
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