Simultaneous similarity classes of commuting matrices over a finite field
نویسندگان
چکیده
منابع مشابه
On types and classes of commuting matrices over finite fields
This paper addresses various questions about pairs of similarity classes of matrices which contain commuting elements. In the case of matrices over finite fields, we show that the problem of determining such pairs reduces to a question about nilpotent classes; this reduction makes use of class types in the sense of Steinberg and Green. We investigate the set of scalars that arise as determinant...
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We consider the solvability of the equation k Yi=1Aixi = B and generalizations, where the Ai and B are given commutingmatrices over an algebraic number eld F . In the semigroup membership problem, the variables xi are constrained to be nonnegative integers. While this problem is NP-complete for variable k, we give a polynomial time algorithm if k is xed. In the group membership problem, the mat...
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In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.
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We study simultaneous block-diagonalization of cyclic d-tuples of commuting matrices. Some application to ideal projectors are also presented. In particular we extend Hans Stetters theorem characterizing Lagrange projectors. 1 Introduction Let V be a nite-dimensional space over complex eld C and let L := (L1; :::; Ld) be a d-tuple of pairwise commuting operators on V . Every polynomial p(x1;...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.03.015