Abstract
In this study, the gradation of involutive matrices, whose definitions were given before, is conducted.The solutions of the equationx2=1 in real numbers are1. Meanwhile, in the solution of the equationxk=1in real numbers, there is always the number1 that is independent of the power ofk2Z+. This feature, which isrevealed by this equation in real numbers, is the subject of the research. In particular, the kind of situation in whichthe equation would display in the matrices is determined. Initially, the second-order square matrices are studied byobtaining some of their properties. Then, new cases arising from the known addition, subtraction, multiplication,scalar multiplication, and division operations of this set of second-order and quadratic involutive matrices areinvestigated. Some properties of third- and second-degree involutive matrices, which can be provided and exist,are emphasized. Comparisons are performed on the involutive matrices. Examples, theorems, and lemmas emergingbetween these two types of matrices are given. New concepts are introduced to the literature by using linear matrixequations and multiplications by the matrices
Recommended Citation
KELE ̧S, Hasan and Hussain, Basaad Ali
(2023)
"On the Involutive Matrices of the kth Degree,"
Iraqi Journal for Computer Science and Mathematics: Vol. 4:
Iss.
1, Article 2.
DOI: https://doi.org/10.52866/ijcsm.2023.01.01.002
Available at:
https://ijcsm.researchcommons.org/ijcsm/vol4/iss1/2
