A resolution of Paz's conjecture in the presence of a nonderogatory matrix

DOI10.1016/j.laa.2018.01.002zbMath1382.15027OpenAlexW2782008718WikidataQ123020949 ScholiaQ123020949MaRDI QIDQ1698600

Helena Šmigoc, O. V. Markova, Thomas J. Laffey, Alexander E. Guterman

Publication date: 16 February 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.01.002

zbMATH Keywords

finite-dimensional algebrasJordan canonical formlengths of sets and algebrasnonderogatory matricesPaz's conjecture

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Algebraic systems of matrices (15A30) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Canonical forms, reductions, classification (15A21)

Related Items (22)

The lengths of matrix incidence algebras over small finite fields ⋮ Generating systems of the full matrix algebra that contain nonderogatory matrices ⋮ On the length of the group algebra of the dihedral group in the semi-simple case ⋮ On the lengths of group algebras of finite abelian groups in the semi-simple case ⋮ An example of length computation for a group algebra of a noncyclic abelian group in the modular case ⋮ Length realizability for pairs of quasi-commuting matrices ⋮ On the lengths of matrix incidence algebras with radicals of square zero ⋮ On generators of incidence rings over finite posets ⋮ Length function and simultaneous triangularization of matrix pairs ⋮ Values of the length function for nonassociative algebras ⋮ The length of a direct sum of nonassociative algebras ⋮ Commutativity of matrices up to a matrix factor ⋮ IRREDUCIBLE FAMILIES OF COMPLEX MATRICES CONTAINING A RANK-ONE MATRIX ⋮ On real algebras generated by positive and nonnegative matrices ⋮ The lengths of group algebras of small-order groups ⋮ Systems of generators of matrix incidence algebras over finite fields ⋮ An improved bound for the lengths of matrix algebras ⋮ Algebras of length one ⋮ -MINIMUM SPANNING LENGTHS AND AN EXTENSION TO BURNSIDE’S THEOREM ON IRREDUCIBILITY ⋮ Upper bounds for the length of non-associative algebras ⋮ THE SLOT LENGTH OF A FAMILY OF MATRICES ⋮ Algebras of slowly growing length

Cites Work

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• ON THE LENGTHS OF PAIRS OF COMPLEX MATRICES OF SIZE SIX
• An application of the Cayley-Hamilton theorem to matrix polynomials in several variables
• The algebra generated by two commuting matrices
• A Theorem of Burnside on Matrix Rings
• On the lengths of pairs of complex matrices of size at most five
• \(C^*\)-algebras by example

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