Weak Spectral Inverses
J. F. Ward, Thomas L. Boullion, Truman O. Lewis · SIAM Journal on Applied Mathematics · 1972
The notion of a weak spectral inverse of a square matrix is introduced, generalizing the definition of a spectral inverse given by Greville. A representation for weak spectral inverses in terms of the Drazin inverse is developed, and it is shown that a formula given previously for the Cline inverse is a special case. Necessary and sufficient conditions are given for a weak spectral inverse to be a spectral inverse, first in terms of the Drazin inverse representation, and then by making use of the quasi-commuting inverse defined by Erdélyi.