The rank of a commutator

DOI10.1080/03081088308817514zbMath0518.15005OpenAlexW2013879759MaRDI QIDQ3667018

Charles Lanski, Robert M. Guralnick

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1080/03081088308817514

zbMATH Keywords

reductiondivision ringmatrix commutatorsminimal rankcompanion matricesirreducible characteristic polynomialmodules over principal ideal domains

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Commutativity of matrices (15A27) Commutators, derivations, elementary operators, etc. (47B47) Commutator calculus (20F12)

Related Items (9)

On the number of invariant polynomials of matrix commutators ⋮ Covering GL(V) and products of blockcyclic matrices ⋮ A quantum-trace determinantal formula for matrix commutators, and applications ⋮ Eigenvalues of matrix commutators^∗ ⋮ INVERTIBLE COMMUTATORS IN MATRIX RINGS ⋮ On similarity invariants of matrix commutators ⋮ On similarity invariants of matrix commutators and Jordan products ⋮ Linear rank one preservers between spaces of matrices with zero trace ⋮ On the invariant polynomials of Jordan products

Cites Work

• A rational canonical pair form for a pair of symmetric matrices over an arbitrary field F with char F ≠ 2 and applications to finest simultaneous block diagonalizations
• A basis theorem for matrix algebras

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