On invertible matrices over antirings

DOI10.1016/j.laa.2007.01.018zbMath1121.15019OpenAlexW2007760089MaRDI QIDQ880048

Yi-Jia Tan

Publication date: 10 May 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.01.018

zbMATH Keywords

permanentmatrix equationCramer's ruleinvertible matrixBoolean matricessemiringfuzzy matricesantiringlattice matricesincline matrices

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)

Related Items (25)

Invertible matrices over a class of semirings ⋮ Minimal orderings and quadratic forms on a free module over a supertropical semiring ⋮ On invertible matrices over commutative semirings ⋮ Decompositions of modules lacking zero sums ⋮ The further study of semimodules over commutative semirings ⋮ Dimensional formulas of semilinear subspaces over semirings ⋮ Inner products on semimodules over a commutative semiring. ⋮ Invertible matrices and semilinear spaces over commutative semirings ⋮ Bases in semilinear spaces over zerosumfree semirings ⋮ On matrices over an arbitrary semiring and their generalized inverses ⋮ Semiring isomorphisms and automorphisms of matrix algebras ⋮ Bases in semimodules over commutative semirings ⋮ Invertible matrices over finite additively idempotent semirings ⋮ \((\alpha ,\beta )\)-intuitionistic fuzzy ideals of hemirings ⋮ A study on characteristic roots of lattice matrices ⋮ Invertible and nilpotent matrices over antirings ⋮ Standard orthogonal vectors in semilinear spaces and their applications ⋮ Inner products on semimodules ⋮ Noncommuting graphs of matrices over semirings ⋮ Commuting graphs of matrices over semirings. ⋮ Unnamed Item ⋮ The bideterminants of matrices over semirings ⋮ Generalized fuzzy \(h\)-bi-ideals and \(h\)-quasi-ideals of hemirings. ⋮ Determinants of matrices over semirings ⋮ Algebras with a negation map

Cites Work

• Inversion of matrices over a commutative semiring
• Linear and combinatorial optimization in ordered algebraic structures
• Linear operators strongly preserving \(r\)-potent matrices over semirings
• Inverses of L-fuzzy matrices
• A generalization of the all minors matrix tree theorem to semirings
• Bideterminants, arborescences and extension of the matrix-tree theorem to semirings
• Matrices over semirings
• Determinantal identities over commutative semirings
• Indices and periods of incline matrices
• Triangular norms
• The semigroup of Hall matrices over distributive lattices
• A regularity criterion for complete matrix semirings
• Invertible incline matrices and Cramer's rule over inclines
• Lattice matrices
• A Note on Boolean Matrix Theory
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