Commutative matrix subalgebras and length function

DOI10.1016/j.laa.2008.07.010zbMath1160.13016OpenAlexW2034425953MaRDI QIDQ1006029

O. V. Markova, Alexander E. Guterman

Publication date: 17 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.07.010

zbMATH Keywords

finite-dimensional algebrascommutative matrix algebrasmatrix length

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Commutativity of matrices (15A27) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items (26)

The effect of assuming the identity as a generator on the length of the matrix algebra ⋮ Lengths of quasi-commutative pairs of matrices ⋮ The realizability problem for the values of the length function of quasi-commuting matrix pairs ⋮ The length function and matrix algebras ⋮ The lengths of the quaternion and octonion algebras ⋮ Commutative nilpotent subalgebras with nilpotency index \(n-1\) in the algebra of matrices of order \(n\) ⋮ 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 ⋮ Classification of matrix subalgebras of length 1. ⋮ Length realizability for pairs of quasi-commuting matrices ⋮ On the lengths of matrix incidence algebras with radicals of square zero ⋮ Extremal matrix centralizers ⋮ Values of the length function for nonassociative algebras ⋮ A resolution of Paz's conjecture in the presence of a nonderogatory matrix ⋮ The length of a direct sum of nonassociative algebras ⋮ Commutativity of matrices up to a matrix factor ⋮ On the relationship between the length of an algebra and the index of nilpotency of its Jacobson radical. ⋮ On some properties of the length function. ⋮ Lengths of cyclic algebras and commutative subalgebras of quaternion matrices ⋮ The algebra of semimagic matrices and its length ⋮ Maximal and minimal triangular matrices ⋮ Characterization of commutative matrix subalgebras of maximal length over an arbitrary field ⋮ Characteristic sequences of non-associative algebras ⋮ Maximal commutative subalgebras of a Grassmann algebra ⋮ Algebras of length one ⋮ Upper bounds for the length of non-associative algebras

Cites Work

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• The theory of matrix polynomials and its application to the mechanics of isotropic continua
• Further results in the theory of matrix polynomials
• The minimal dimension of maximal commutative subalgebras of full matrix algebras
• An upper bound for the length of a finite-dimensional algebra
• The dimension of maximal commutative subalgebras of \(K_ n\)
• On dominance and varieties of commuting matrices
• Two-generated commutative matrix subalgebras
• An application of the Cayley-Hamilton theorem to matrix polynomials in several variables
• The algebra generated by two commuting matrices
• Matrix Analysis
• Maximal Commutative Subalgebras ofn×nMatrices
• On the length of the algebra of upper-triangular matrices

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