2 papers
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.CO2022
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…