Determinantal identities over commutative semirings

DOI10.1016/j.laa.2004.02.019zbMath1057.15009OpenAlexW2047285205MaRDI QIDQ1434389

Robert E. Hartwig, Phillip L. Poplin

Publication date: 4 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.laa.2004.02.019

zbMATH Keywords

compound matricesdeterminantdeterminantal identitiescommutative semiringsadjoint matrix identitiesCauchy-Binet theoremLaplace theorem

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Endomorphism rings; matrix rings (16S50) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)

Related Items (26)

A separation between tropical matrix ranks ⋮ On invertible matrices over commutative semirings ⋮ On ranks, Green classes, and the theory of determinants of Boolean matrices ⋮ New necessary and sufficient condition and algorithm for directed hamiltonian graph based on boolean determinant theory ⋮ On simultaneously nilpotent antiring matrices ⋮ Dimensional formulas of semilinear subspaces over semirings ⋮ Determinant theory for lattice matrices ⋮ On invertible matrices over antirings ⋮ The cardinality of bases in semilinear spaces over commutative semirings ⋮ Invertible matrices and semilinear spaces over commutative semirings ⋮ Bases in semilinear spaces over zerosumfree semirings ⋮ Tropical patterns of matrices and the Gondran-Minoux rank function ⋮ Tan's epsilon-determinant and ranks of matrices over semirings ⋮ Lattice vector spaces and linear transformations ⋮ On nilpotent matrices over antirings ⋮ Note on the free sets and free subsemimodules in semimodules ⋮ Standard orthogonal vectors in semilinear spaces and their applications ⋮ On nilpotency of matrices over antirings ⋮ Matrix Invariants over Semirings ⋮ The bideterminants of matrices over semirings ⋮ Free sets and free subsemimodules in a semimodule ⋮ On cofactor expansion of determinants of Boolean matrices ⋮ The DJL Conjecture for CP Matrices over Special Inclines ⋮ The applications of the bideterminant of a matrix over commutative semirings ⋮ The solvable conditions of linear system over commutative semirings ⋮ Determinants of matrices over semirings

Cites Work

• Inertia characteristics of self-adjoint matrix polynomials
• Unnamed Item
• Unnamed Item

This page was built for publication: Determinantal identities over commutative semirings