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Submatrix monotonicity of the Perron root

Pisonero, M.
; 
Johnson, C. R.
; 
Marijuan, C.
Abstract
It is known that increasing an entry of a nonnegative matrix non-decreases (and generally increases) its Perron root. Motivated by a question raised by Jose Dias da Silva, we study the partial order on k-by-k nonnegative matrices in which A less than or similar to(DS) B if whenever A and B occur as submatrices in the same position in otherwise equal nonnegative matrices F and G, p (F) < = p (G). We find that this partial order is equivalent to the entry-wise partial order. This is proven with some asymptotic results about the Perron root that may be of independent interest. (C) 2012 Elsevier Inc. All rights reserved.
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2012-01-01
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Mathematics
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Mathematics
DOI
10.1016/j.laa.2012.07.006
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https://scholarworks.wm.edu/handle/internal/769
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