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On nonnegative matrices similar to positive matrices

✍ Scribed by Alberto Borobia; Julio Moro

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
764 KB
Volume
266
Category
Article
ISSN
0024-3795

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✦ Synopsis

We

prove that 2" is star-shaped with respect to (1, 0, . . . , 0) and that (1, A,, . . . , A,) ~j" is on the boundary of 2" if and only if 11, A,, . . . , A,) is not the spectrum of any positive matrix. As a consequence, attention is given to the problem of determining which nonnegative matrices are similar to positive ones. More precisely, we address the question of which pattern matrices P satisfy that any nonnegative matrix with pattern P is similar to a positive matrix. Some partial results are obtained (among them that any irreducible nonnegative matrix with a positive line is similar to a positive matrix), which allow us to give a complete solution to the case of S-by-3 matrices.

πŸ“œ SIMILAR VOLUMES

A characterization of Jordan canonical f
A characterization of Jordan canonical forms which are similar to eventually nonnegative matrices with the properties of nonnegative matrices
✍ Boris G Zaslavsky; Judith J McDonald πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 282 KB

In this paper we give necessary and sufficient conditions for a matrix in Jordan canonical form to be similar to an eventually nonnegative matrix whose irreducible diagonal blocks satisfy the conditions identified by Zaslavsky and Tam, and whose subdiagonal blocks (with respect to its Frobenius norm