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

Abstract

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.

Keywords

• matrix square root
• quartic polynomial equation
• characteristic polynomial
• jordan canonical form
• primary: 15a23. secondary: 11c20