Page 116 - Textos de Matemática Vol. 44
P. 116
106 N. KRUPNIK AND Y. SPIGEL
Thus Theorem 6.11 describes all fourth-degree polynomials F(A,B) which satisfy the condition of Theorem 2.1 with degF1 = degF2. Namely, one can take an arbitrary two-degree polynomial G(A, B) and compose the polynomial (6.13).
We conclude this paper with an open
Problem 6.13. It would be interesting to obtain a complete description of all admissible polynomials of degrees n ≥ 4.
References
[1] F. R. Gantmacher, The Theory of Matrices V.1, Chelsa Pub. Comp. N.Y, (1960)
[2] I. Gohberg, S. Goldberg, N. Krupnik, Traces and Determinants of Linear Operators,
OTAA Vol. 116, Birkha¨user, 2000.
[3] L. L. Pennisi, Coefficients of the Characteristic Polynomial, Math. Magazine 60
(Feb. 1981), no. 1, pp. 31 - 33.
(N. Krupnik) 208 - 7460 Bathurst str, Thornhill, Ontario, L4J 7K9, Canada E-mail address: krupnik13@rogers.com
(Y. Spigel) 407 - 333 Clark ave, Thornhill, Ontario, L4J 3E7, Canada E-mail address: shpigel@gmail.com
