Boonrod Yuttanan and Chaufah Nilrat

pp. 659 - 665

Abstract

A matrix S is said to be an n^th root of a matrix A if Sⁿ
 = A, where n is a positive integer greater than or
equal to 2. If there is no such matrix for any integer n ≥ 2, A is called a rootless matrix. After investigating
the properties of these matrices, we conclude that we always find an n^th root of a non-singular matrix and
a diagonalizable matrix for any positive integer n. On the other hand, we find some matrix having an n^th root
for some positive integer n. We call it p-nilpotent matrix.