# 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.

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Capsule Course Topic(s):
Linear Algebra | Determinants
Linear Algebra | Matrix Algebra