On the square root of quadratic matrices

Subject Areas : Linear and multilinear algebra; matrix theory

A.  Zardadi ¹ (Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-4697, Tehran, Iran)

Received: 2019-02-10 Accepted : 2019-07-02 Published : 2019-08-01

Keywords: eigenvalue, matrix equation, Square root of matrix,

Abstract :

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2\times 2$ matrices.

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