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Square roots of real \(3 \times 3\) matrices vs. quartic polynomials with real zeros. (English) Zbl 1424.15013

Summary: There is an interesting analogy between the description of the real square roots of \(3\times 3\) 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.

MSC:

15A16 Matrix exponential and similar functions of matrices
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
26C10 Real polynomials: location of zeros
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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