SFB 303 Discussion Paper No. B - 134
Author: Neumann, Michael, and Hans Joachim Werner
Title: Nonnegative Group Inverses
Abstract: For a nonnegative block lower triangular matrix we
characterize when it possesses a nonnegative group inverse
and, when it does, we give this inverse an explicit formula.
As a consequence we show that a necessary condition for the
existence of such an inverse is that the eigenspace of the
matrix corresponding to its Perron root is spanned by
eigenvectors only. Actually we deduce a stronger result.
Namely, that a necessary condition for a nonnegative matrix
to have a nonnegative Drazin inverse is that its eigenspace
corresponding to its Perron root is spanned by eigenvectors
Keywords: Nonnegativity, group inverse, Drazin inverse
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