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A matrix-decomposition theorem for GLn (K)
Publikationstyp
Journal Article
Date Issued
1999-09-01
Sprache
English
Author(s)
TORE-URI
Volume
298
Issue
1-3
Start Page
39
End Page
50
Citation
Linear Algebra and Its Applications 1-3 (298): 39-50 (1999-09-01)
Publisher DOI
Scopus ID
Publisher
American Elsevier Publ.
Given an arbitrary commutative field K, n ∈ ℕ≥3 and two monic polynomials q and r over K of degree n - 1 and n such that q(0) ≠ 0 ≠ r(0). We prove that any non-scalar invertible n x n matrix M can be written as a product of two matrices A and B, where the minimum polynomial of A is divisible by q and B is cyclic with minimum polynomial r. This result yields that the Thompson conjecture is true for PSLn(F3), n ∈ ℕ≥3, and PSL2n+1(F2), n ∈ ℕ. If G is such a group, then G has a conjugacy class Ω such that G = Ω2. In particular each element of G is a commutator.
Subjects
Conjugacy class
Matrix factorization
Product of cyclic matrices
DDC Class
004: Informatik
510: Mathematik