On the square root of quadratic matrices

Subject Areas : Linear and multilinear algebra; matrix theory

A. Zardadi ¹

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.

References:

[1] G. Alefeld, N. Schneider, On square roots of M-matrices, Linear. Algebra. Appl. 42 (1982), 119-132.

[2] E. D. Denman, A. N. Beavers, The matrix sign function and computations in systems, Appl. Math. Comput. 2 (1) (1976), 63-94.

[3] W. D. Hoskins, D. J. Walton, A faster method of computing the square root of a matrix, IEEE Trans. Automat. Control. 23 (3) (1978), 494-495.

[4] B. W. Levinger, The square root of a 2 × 2 matrix, Math. Mag. 53 (4) (1980), 222-224.

[5] A. Nazari, H. Fereydooni, M. Bayat, A manual approach for calculating the root of square matrix of dimension, Math. Sci. 7 (1) (2013), 1-6.

[6] D. Sullivan, The square roots of 2 × 2 matrices, Math. Mag. 66 (5) (1993), 314-316.