4 papers
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…
A "power" conjugate equation in the symmetric group
Szilvia Homolya, Jenő Szigeti
First we consider the solutions of the general "cubic" equation a_{1}x^{r1}a_{2}x^{r2}a_{3}x^{r3}=1 (with r1,r2,r3 in {1,-1}) in the symmetric group S_{n}. In certain cases this eq…
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…
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).