# The Square Roots of $2 \times 2$ Matrices

by Donald Sullivan (University of New Brunswick, Canada)

Mathematics Magazine
December, 1993

Subject classification(s): Algebra and Number Theory | Linear Algebra | Matrix Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra | 4.13 Advanced Linear Algebra

The Cayley-Hamilton theorem may be used to determine explicit formulae for all the square roots of $2 \times 2$ matrices. These formulae indicate exactly when a $2 \times 2$ matrix has square roots, and the number of such roots.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.