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Universal algorithms for solving the matrix Bellman equations over semirings [PDF]
Soft Computing, 2013 40 pages.
Sergeĭ Sergeev, Andrei N Sobolevski
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Journal of Mathematical Sciences, 2006
In classical ring theory there are many results containing different algebraic conditions which force an arbitrary ring to be a full matrix ring. This paper deals with similar conditions which force a semiring \(S\) to be a matrix semiring over some different semiring \(R\).
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In classical ring theory there are many results containing different algebraic conditions which force an arbitrary ring to be a full matrix ring. This paper deals with similar conditions which force a semiring \(S\) to be a matrix semiring over some different semiring \(R\).
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Factoring a band matrix over a semiring
Fuzzy Sets and Systems, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Application of tropical semiring for matrix factorization
Uporabna informatika, 2020Matrix factorization methods employ standard linear algebra, i.e. linear models, for recommender systems. With the introduction of the tropical semiring, we can achieve non-linearity. We review algorithms that use the tropical semiring for matrix factorization and provide their strengths and limitations.
Amra Omanović +2 more
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On matrix semiring over the extended tropical semiring
Asian-European Journal of MathematicsIn this paper, we first discuss about the basic semiring properties; subsemirings, ideals, [Formula: see text]-ideals, [Formula: see text]-ideals, units, structure preserving properties of both extended tropical semiring [Formula: see text] and semiring of tropical matrices [Formula: see text]. Using the known fact that the subsemimodules of [Formula:
Bikramjit Roy +3 more
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Endomorphisms of upper triangular matrix semirings
Communications in Algebra, 2021We give a description of the class of endomorphisms in the semiring UTMn(S) of upper triangular matrices over an additively idempotent semiring S.
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Regularity Criterion for Complete Matrix Semirings
Mathematical Notes, 2001Let \((S,+,\cdot)\) be an additively commutative semiring with absorbing zero 0. \(S\) is regular if for every \(a\in S\) the equation \(axa=a\) is solvable in \(S\). It is shown, that for \(n\geq 3\) the semiring \(M_n(S)\) of all \(n\times n\)-matrices over \(S\) is regular iff \(S\) is a regular ring.
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Semiring Isomorphisms and Automorphisms of Matrix Algebras
Journal of Mathematical Sciences, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Derivations of upper triangular matrix semirings
Linear and Multilinear Algebra, 2020In this paper, the author gives a description of the derivatives in UTMn(S), the semiring of upper triangular matrices over an additively idempotent semiring S.
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The applications of the bideterminant of a matrix over commutative semirings
Linear and Multilinear Algebra, 2016AbstractThis paper discusses some applications of the bideterminant of a matrix over commutative semirings. It first uses the bideterminant of a matrix to define the McCoy rank of a matrix and gives some necessary and sufficient conditions that the McCoy rank of an matrix is less than n.
Qian-yu Shu, Xue-ping Wang
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