Akademik Veri Yönetim Sistemi
Iraqi Journal for Computer Science and Mathematics, cilt.4, sa.1, ss.10-14, 2022 (Scopus)
In this study, the gradation of involutive matrices, whose definitions
were given before, is conducted. The solutions of the equation x2 = 1 in
real numbers are ±1. Meanwhile, in the solution of the equation xk = 1
in real numbers, there is always the number ±1 that is independent of
the power of k 2 Z+. This feature, which is revealed by this equation in
real numbers, is the subject of the research. In particular, the kind
of situation in which the equation would display in the matrices is
determined. Initially, the second-order square matrices are studied by
obtaining 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 are investigated. 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 emerging
between these two types of matrices are
given. New concepts are introduced to the literature by using linear
matrix equations and multiplications by the matrices