Roots of Matrices

Abstract

A matrix S is said to be an nth 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 nth 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 nth root for some positive integer n. We call it p-nilpotent matrix.

Keywords

• roots of matrices
• rootless matrix
• nilpotent matrix
• non-singular matrix
• diagonalizable matrix