# Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring

Serdica Mathematical Journal (2006)

- Volume: 32, Issue: 2-3, page 269-276
- ISSN: 1310-6600

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topSzigeti, Jeno. "Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring." Serdica Mathematical Journal 32.2-3 (2006): 269-276. <http://eudml.org/doc/281373>.

@article{Szigeti2006,

abstract = {2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.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.},

author = {Szigeti, Jeno},

journal = {Serdica Mathematical Journal},

keywords = {Commutator Subgroup [R,R] of a Ring R; Cayley-Hamilton theorem; preadjoint of matrix; right characteristic polynomial of matrix; commutators of rings},

language = {eng},

number = {2-3},

pages = {269-276},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring},

url = {http://eudml.org/doc/281373},

volume = {32},

year = {2006},

}

TY - JOUR

AU - Szigeti, Jeno

TI - Cayley-Hamilton Theorem for Matrices over an Arbitrary Ring

JO - Serdica Mathematical Journal

PY - 2006

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 32

IS - 2-3

SP - 269

EP - 276

AB - 2000 Mathematics Subject Classification: 15A15, 15A24, 15A33, 16S50.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.

LA - eng

KW - Commutator Subgroup [R,R] of a Ring R; Cayley-Hamilton theorem; preadjoint of matrix; right characteristic polynomial of matrix; commutators of rings

UR - http://eudml.org/doc/281373

ER -

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