Ela Commuting
نویسنده
چکیده
The variety C(3, n) of commuting triples of n × n matrices over C is shown to be irreducible for n = 7. It had been proved that C(3, n) is reducible for n ≥ 30, but irreducible for n ≤ 6. Guralnick and Omladič have conjectured that it is reducible for n > 7.
منابع مشابه
Ela on Maximal Distances in a Commuting Graph
It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.
متن کاملEla Polynomial Inequalities for Non-commuting Operators
We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.
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Let D be a division ring, n 2 a natural number, and C ⊆ Mn(D). Two matrices A and B are called C−commuting if there is C ∈ C that AB−BA = C. In this paper the C−commuting graph of Mn(D) is defined and denoted by ΓC(Mn(D)). Conditions are given that guarantee that the C−commuting graph is connected.
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A class of matrix valued analytic functions of two non-commuting matrices is considered. A sharp norm estimate is established. Applications to matrix and differential equations are also discussed.
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Matrix valued analytic functions of two commuting matrices are considered. A precise norm estimate is established. As a particular case, the matrix valued functions of two matrices on tensor products of Euclidean spaces are explored.
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