Principal Components of Minus M-Matrices
Technical summary rept.
WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES
Pagination or Media Count:
This paper determines the nonnegativity of the principal components of an n x n nonnegative matrix P in terms of the marked reduced graph RA of A P - rhoPI, the minus M matrix which can be associated with P. We then apply this result to consider various types of nonnegative bases for the Perron eigenspace of P which can be extracted from a certain nonnegative matrix which is a polynomial in P. We also obtain a characterization for the eigenprojection on the Perron eigenspace of P to be, itself, a nonnegative matrix. Our results provide new proofs and extensions of results of Friedland and Schneider and of Hartwig, Neumann, and Rose.
- Numerical Mathematics