Some basic properties of idempotent matrices

Hammodat, Alaa A.; Bilal, Ali A.; Mohammed, Akram S.

doi:10.33899/edusj.2008.56102

Cited by 1 publication

(1 citation statement)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While studying prime matrices, I came to the conclusion that known involutive matrices may involve degrees. The generalized definition of involution is given below [2,4,[10][11][12]14]. The generalized definition of involutive is given below.…”

Section: Involutive Matrices Of the K Th Degreementioning

confidence: 99%

On the Involutive Matrices of the kth Degree

2022

ijcsm

View full text Add to dashboard Cite

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

show abstract

Section: Involutive Matrices Of the K Th Degreementioning

confidence: 99%

On the Involutive Matrices of the kth Degree

2022

ijcsm

View full text Add to dashboard Cite

show abstract

Some basic properties of idempotent matrices

Abstract: In this paper we give some properties of the zero commut idempotent matrices ,and give some properties of non-singular matrices. Some basic properties of idempotent matrices.

Cited by 1 publication

References 1 publication

On the Involutive Matrices of the kth Degree

On the Involutive Matrices of the kth Degree

Contact Info

Product

Resources

About