Invertible matrices and semilinear spaces over commutative semirings

DOI10.1016/j.ins.2010.08.033zbMath1207.15009OpenAlexW2072854112MaRDI QIDQ621619

Shan Zhao, Xue-ping Wang

Publication date: 28 January 2011

Published in: Information Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ins.2010.08.033

zbMATH Keywords

basislinear independenceinvertible matrixcommutative semiringsemilinear space

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Semirings (16Y60) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (25)

Invertible matrices over a class of semirings ⋮ Orthogonal complements and extending orthogonal subsets of semimodules ⋮ The further study of semimodules over commutative semirings ⋮ Dimensional formulas of semilinear subspaces over semirings ⋮ The total graphs of finite commutative semirings ⋮ The cardinality of bases in semilinear spaces over commutative semirings ⋮ The automorphism group of the zero-divisor digraph of matrices over an antiring ⋮ Inner products on semimodules over a commutative semiring. ⋮ The metric dimension of the zero-divisor graph of a matrix semiring ⋮ The unitary Cayley graph of a semiring ⋮ Bases in semilinear spaces over join-semirings ⋮ Bases in semilinear spaces over zerosumfree semirings ⋮ Note on cardinality of bases in semilinear spaces over zerosumfree semirings ⋮ Bases in semimodules over commutative semirings ⋮ Solution sets of finite fuzzy relation equations with sup-inf composition over bounded Brouwerian lattices ⋮ Lattice vector spaces and linear transformations ⋮ Cholesky decomposition of matrices over commutative semirings ⋮ Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations ⋮ Zero-divisor graph of direct products of matrices over semirings ⋮ Standard orthogonal vectors in semilinear spaces and their applications ⋮ Inner products on semimodules ⋮ The bideterminants of matrices over semirings ⋮ Free sets and free subsemimodules in a semimodule ⋮ The applications of the bideterminant of a matrix over commutative semirings ⋮ Extension of free sets over commutative semirings

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