Term-rank, permanent, and rook-polynomial preservers
type: Item
instance of: scholarly article
title: Term-rank, permanent, and rook-polynomial preservers
zbMATH Open document ID: 0617.15001
DOI: 10.1016/0024-3795(87)90302-8
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The term-rank is the least \(x+y\) such that x rows and y columns cover all nonzero entries in a matrix. The authors show that linear transformations over any semiring preserve term-rank if and only if they are compositions of permutations of rows and columns, transpose, and entrywise multiplication by another matrix. They obtain a similar characterization of transformations preserving permanent.
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 4000122
zbMATH Keywords: term-rank preserving transformation
zbMATH Keywords: rook-polynomial preserving operators
zbMATH Keywords: semirings
zbMATH Keywords: nonnegative integer matrices
zbMATH Keywords: fuzzy matrices
zbMATH Keywords: linear transformations
zbMATH Keywords: permanent
author: Leroy B. Beasley
author: Norman J. Pullman
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90302-8
OpenAlex ID: W2037645984
cites work: Boolean-rank-preserving operators and Boolean-rank-1 spaces
cites work: Fuzzy rank-preserving operators
cites work: Nonnegative rank-preserving operators
cites work: Q3758977
cites work: Q3958592
cites work: The Permanent Function
cites work: Linear Transformations on Algebras of Matrices
cites work: Transformations on tensor product spaces
cites work: 𝑅-linear endomorphisms of (𝑅)_{𝑛} preserving invariants
cites work: Q3851094
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description: scientific article; zbMATH DE number 4000122