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

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

[2] H. F. Baker, The Reciprocation of One Quadric into Another, Proc. Cambridge Philos. Soc. 23, 22-27, (1925).10.1017/S0305004100012020Search in Google Scholar

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

[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).10.1017/S0370164600042887Search in Google Scholar

[5] G. W. Cross, P. Lancaster Square Roots of Complex Matrices, Lin. Multilin. Alg. 1, 289-293, (1974).10.1080/03081087408817029Search in Google Scholar

[6] G. Frobenius, Über die cogredienten Transformationen der bilinearen Formen, Sitzungsber K. Preuss. Akad. Wiss. Berlin, 16, 7-16, (1896).Search in Google Scholar

[7] N. H. Higham, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, PA (2008).Search in Google Scholar

[8] R. A. Horn, C. R. Johnson Topics in Matrix Analysis, Cambridge Univ. Press, Cambridge (1991).10.1017/CBO9780511840371Search in Google Scholar

[9] B. W. Levinger, The Square Root of a 2 × 2 Matrix, Math. Magazine 53, No. 4, 222-224, (1980).10.1080/0025570X.1980.11976858Search in Google Scholar

[10] W. H. Metzler, On the Roots of Matrices, Amer. J. Math. 14, No. 4, 326-377, (1892).10.2307/2369610Search in Google Scholar

[11] E. L. Rees, Graphical Discussion of the Roots of a Quartic Equation, Amer. Math. Monthly 29, No. 2, 51-55, (1922).10.1080/00029890.1922.11986100Search in Google Scholar

[12] H. E. Salzer, A Note on the Solution of Quartic Equations, Math. Comp. 14, No. 71, 279-281, (1960).10.1090/S0025-5718-1960-0117882-6Search in Google Scholar

[13] I. Stewart, Galois Theory, 2nd Edition, Chapman & Hall, London (1989).10.1007/978-94-009-0839-0Search in Google Scholar

[14] D. Sullivan, The Square Roots of 2×2 Matrices, Math. Magazine 66, No. 5, 314-316, (1993). 10.1080/0025570X.1993.11996153Search in Google Scholar

[15] H. Taber, On the Theory of Matrices, Amer. J. Math. 12, No. 4, 337- 396, (1890).10.2307/2369849Search in Google Scholar

[16] Wikipedia Contributors, Quartic Function, Wikipedia, The Free En- cyclopedia, https:/en.wikipedia.org/wiki/Quartic_functionSearch in Google Scholar