Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3338
Abstract
Let $A_{1}$ and $A_{2}$ be an $\{\alpha_{1}, \beta_{1}, \gamma_{1}\}$-cubic matrix and an $\{\alpha_{2}, \beta_{2}\}$-quadratic matrix, respectively, with $\alpha_{1} \neq \beta_{1}$, $\beta_{1} \neq \gamma_{1}$, $\alpha_{1} \neq \gamma_{1}$ and $\alpha_{2}\neq \beta_{2}$. In this work, we characterize all situations in which the linear combination $A_{3}=a_{1}A_{1}+a_{2}A_{2}$ with the assumption $A_{1}A_{2}=A_{2}A_{1}$ is an $\{\alpha_{3}, \beta_{3}\}$-quadratic matrix, where $a_{1}$ and $a_{2}$ are unknown nonzero complex numbers.
Keywords
Quadratic matrix, cubic matrix, linear combination, diagonalization
First Page
3373
Last Page
3390
Recommended Citation
PETİK, TUĞBA; ÖZDEMİR, HALİM; and GÖKMEN, BURAK TUFAN
(2022)
"Notes on the quadraticity of linear combinations of a cubic matrix and a quadratic matrix that commute,"
Turkish Journal of Mathematics: Vol. 46:
No.
8, Article 20.
https://doi.org/10.55730/1300-0098.3338
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss8/20
