Matrices whose characteristic equations are cyclic
نویسندگان
چکیده
منابع مشابه
Finite groups all of whose proper centralizers are cyclic
A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic. In this article we determine all finite $CC$-groups.
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A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$. It is not known whether a direct summand of an FI-extending module is also FI-extending. In this study, it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?
متن کاملOn Matrices Whose Real Linear Combinations Are Nonsingular
Let A be either the real field R, or the complex field C, or the skew field Q of quaternions. Let Au A2, • ■ ■ , Ak be nXn matrices with entries from A. Consider a typical linear combination E"-iV^> with real coefficients Xy; we shall say that the set {A¡} "has the property P" if such a linear combination is nonsingular (invertible) except when all the coefficients X> are zero. We shall write A...
متن کاملCorrection to "on Matrices Whose Real Linear Combinations Are Nonsingular"
2. -, Rings with a pivotal monomial, Proc. Amer. Math. Soc. 9 (1958), 635642. 3. L. P. Belluce and S. K. Jain, Prime rings having a one-sided ideal satisfying a polynomial identity, Abstract 614-89, Notices Amer. Math. Soc. 11 (1964), p. 554. 4. N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Publ. Vol. 37, Amer. Math. Soc, Providence, R. I., 1956. 5. I. Kaplansky, Rings with a polyno...
متن کاملLiapunov Exponents for Higher-order Linear Differential Equations Whose Characteristic Equations Have Variable Real Roots
We consider the linear differential equation n X k=0 ak(t)x (n−k)(t) = 0 t ≥ 0, n ≥ 2, where a0(t) ≡ 1, ak(t) are continuous bounded functions. Assuming that all the roots of the polynomial zn + a1(t)zn−1 + · · · + an(t) are real and satisfy the inequality rk(t) < γ for t ≥ 0 and k = 1, . . . , n, we prove that the solutions of the above equation satisfy |x(t)| ≤ const eγt for t ≥ 0.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1930
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1930-04930-7