Results 31 to 40 of about 148 (49)
On maximal distances in a commuting graph [PDF]
, 2010 We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular, we show that the maximal distance can be attained only between two nonderogatory matrices.
Dolinar, Gregor +2 more
core
Representation of tripotents and representations via tripotents [PDF]
, 2011 Let A be an algebra. An element A∈A is called tripotent if A3=A. We study the questions: if both A and B are tripotents, then: Under what conditions are A+B and AB tripotent? Under what conditions do A and B commute?
Bikchentaev A., Yakushev R.
core +1 more source
Sylvester matrix and common factors in polynomial matrices [PDF]
, 2007 With the coefficient matrices of the polynomial matrices replacing the scalar coefficients in the standard Sylvester matrix, common factors exist if and only if this (generalized) Sylvester matrix is singular and the coefficient matrices commute.
Wegge , Leon
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The kernels of powers of linear operator via Weyr characteristic
, 2023 The adjoint of a matrix in the Lie algebra associated with a matrix algebra is a fundamental operator, which can be generalized to a more general operator $\varphi_{AB}: X\rightarrow AX-XB$ by two matrices $A$ and $B$.
Jian, Jie, Liao, Jun, Liu, Heguo
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Commuting Jordan Types: a Survey
, 2023 In this paper, we survey the progress in the problem of finding the maximum commuting nilpotent orbit that intersects the centralizer of a given nilpotent matrix.Comment: 17 Pages, 4 ...
Khatami, Leila
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On the diameter of the commuting graph of the full matrix ring over the real numbers [PDF]
, 2017 In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring Mn(R) is equal to 4 if either n = 3 or n = 5. But the case n = 4 remained open, since the diameter could be 4 or 5.
Grau, J.M. +2 more
core +1 more source
Diameters of commuting graphs of matrices over semirings
, 2010 We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring.
Bukovšek, Damjana Kokol +2 more
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Sylvester Matrix and Common Factors in Polynomial Matrices [PDF]
With the coefficient matrices of the polynomial matrices replacing the scalar coefficients in the standard Sylvester matrix, common factors exist if and only if this (generalized) Sylvester matrix is singular and the coefficient matrices commute.
Leon Wegge
core
One sided Star and Core orthogonality of matrices
, 2023 We investigate two one-sided orthogonalities of matrices, the first of which is left (right) $*$-orthogonality for rectangular matrices and the other is left (right) core-orthogonality of index $1$ matrices.
Ferreyra, D. E. +3 more
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Several Zagreb indices of power graphs of finite non-abelian groups. [PDF]
Heliyon, 2023 Ismail R +5 more
europepmc +1 more source