On invertible matrices over commutative semirings

DOI10.1080/03081087.2012.703191zbMath1266.15011OpenAlexW2062445284MaRDI QIDQ5300057

Yi-Jia Tan

Publication date: 24 June 2013

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

Full work available at URL: https://doi.org/10.1080/03081087.2012.703191

zbMATH Keywords

determinantCramer's ruleinvertible matrixsemiringadjoint matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Semirings (16Y60)

Related Items (12)

Invertible matrices over a class of semirings ⋮ The cardinality of bases in semilinear spaces over commutative semirings ⋮ Analysis of linear systems over idempotent semifields ⋮ On the maximal solution of a linear system over tropical semirings ⋮ On matrices over an arbitrary semiring and their generalized inverses ⋮ Diagonability of matrices over commutative semirings ⋮ Tan's epsilon-determinant and ranks of matrices over semirings ⋮ Cramer’s rule over residue class rings of Bézout domains ⋮ Note on invertible matrices over commutative semirings ⋮ On strongly invertible matrices over semirings ⋮ The applications of the bideterminant of a matrix over commutative semirings ⋮ Determinants of matrices over semirings

Cites Work

• Noncommuting graphs of matrices over semirings
• Commuting graphs of matrices over semirings.
• On invertible matrices over antirings
• Inversion of matrices over a commutative semiring
• Linear operators strongly preserving idempotent matrices over semirings
• Linear operators strongly preserving \(r\)-potent matrices over semirings
• Inverses of L-fuzzy matrices
• Matrices over semirings
• Factorizations of matrices over semirings.
• Determinantal identities over commutative semirings
• Invertible incline matrices and Cramer's rule over inclines
• Maps preserving invertibility of matrices over semirings
• Inversive semirings
• Linear operators strongly preservingr-cyclic matrices over semirings
• Lattice matrices

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