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Title: Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring
Authors: Szigeti, Jeno
Keywords: Commutator Subgroup [R,R] of a Ring R
Issue Date: 2006
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 32, No 2-3, (2006), 269p-276p
Abstract: For an n×n matrix A over an arbitrary unitary ring R, we obtain the following Cayley-Hamilton identity with right matrix coefficients: (λ0I+C0)+A(λ1I+C1)+… +An-1(λn-1I+Cn-1)+An (n!I+Cn) = 0, where λ0+λ1x+…+λn-1 xn-1+n!xn is the right characteristic polynomial of A in R[x], I ∈ Mn(R) is the identity matrix and the entries of the n×n matrices Ci, 0 ≤ i ≤ n are in [R,R]. If R is commutative, then C0 = C1 = … = Cn-1 = Cn = 0 and our identity gives the n! times scalar multiple of the classical Cayley-Hamilton identity for A.
Description: 2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.
ISSN: 1310-6600
Appears in Collections:Volume 32, Number 2-3

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