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On linear preservers of permanental rank

Linear Algebra and its Applications. 2024. Vol. 680. P. 325–340.
Spiridonov I., Guterman A.
Language: English
DOI
Keywords: permanentrank subspace
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Maximal generalized rank in graphical matrix spaces
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Added: October 3, 2024
Permanent Polya problem for additive surjective maps
Guterman A. E., Spiridonov I.A., Linear Algebra and its Applications 2020 Vol. 599 P. 140–155
Let $M_{n}(\mathbb{F})$ denote the set of square matrices  of size $n$ over a field $\mathbb{F}$ with characteristics different from two. We say that the map  $f: M_{n}(\mathbb{F}) \rightarrow M_{n}(\mathbb{F})$ is additive if $f(A+B) = f(A) + f(B)$ for all $A, B \in M_{n}(\mathbb{F})$. The main goal of this paper is to prove that for $n>2$ ...
Added: November 9, 2020
On the linear classification of even and odd permutation matrices and the complexity of computing the permanent
M.N.Vyalyi, Babenko A. V., Computational Mathematics and Mathematical Physics 2017 Vol. 57 No. 2 P. 362–371
The problem of linear classification of the parity of permutation matrices is studied. This problem is related to the analysis of complexity of a class of algorithms designed for computing the permanent of a matrix that generalizes the Kasteleyn algorithm. Exponential lower bounds on the magnitude of the coefficients of the functional that classifies the ...
Added: October 16, 2017
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