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math.RA2025
On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix
Szilvia Homolya, Jenő Szigeti
An nxn matrix A over an arbitrary unitary ring R satisfies invariant left and right Cayley-Hamilton identities with matrix coefficients C(i), D(i) having commutator sum entries. If…
math.RA2021
Lie properties in associative algebras
Szilvia Homolya, Jeno Szigeti, Leon van Wyk +1
Let K be a field, then we exhibit two matrices in the full nxn matrix algebra M_{n}(K) which generate M_{n}(K) as a Lie K-algebra with the commutator Lie product. We also study Lie…
math.RA2020
Z2-graded Cayley-Hamilton trace identities in M_{n}(E)
Szilvia Homolya, Jeno Szigeti
We show, how the combination of the Cayley-Hamilton theorem and a certain companion matrix construction can be used to derive Z2-graded trace identities in M_{n}(E).