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

Author:

Anghel Nicolae1

Affiliation:

1. Department of Mathematics, University of North Texas, Denton , TX 76203, USA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Reference16 articles.

1. [1] N. Anghel, Square Roots of Real 2×2 Matrices, Gazeta Mat. CXVIII, 489-491, (2013).

2. [2] H. F. Baker, The Reciprocation of One Quadric into Another, Proc. Cambridge Philos. Soc. 23, 22-27, (1925).

3. [3] A. Cayley, A Memoir on the Theory of Matrices, Philos. Trans. Roy. Soc. London CXLVIII, 17-37, (1858).10.1098/rstl.1858.0002

4. [4] A. Cayley, On the Extraction of the Square Root of a Matrix of the Third Order, Proc. Roy. Soc. Edinburgh 7, 675-682, (1872).

5. [5] G. W. Cross, P. Lancaster Square Roots of Complex Matrices, Lin. Multilin. Alg. 1, 289-293, (1974).

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