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Abstract There is an interesting analogy between the description of the real square roots of 3×3 matrices and the zeros of the (depressed) real quartic polynomials. This analogy, which in fact better explains the nature of the zeros of those polynomials, is unveiled through a natural use of the Cayley-Hamilton theorem.

Square Roots of Real 3 × 3 Matrices vs. Quartic Polynomials with Real Zeros