The Minimal Polynomial of Some Matrices Via Quaternions
نویسندگان
چکیده
منابع مشابه
extensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولSome results on the polynomial numerical hulls of matrices
In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.
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An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.
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In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.
متن کاملSome Inequalities for Sums of Nonnegative Definite Matrices in Quaternions
The collection of all quaternions is denoted byH and is called the real quaternionic algebra. This algebra was first introduced by Hamilton in 1843 (see [5, 6]), and is often called the Hamilton quaternionic algebra. It is well known thatH is an associative division algebra over R. For any a= a0 + a1i+ a2 j + a3k ∈H, the conjugate of a = a0 + a1i + a2 j + a3k is defined to be a = a0 − a1i− a2 j...
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ژورنال
عنوان ژورنال: Advances in Applied Clifford Algebras
سال: 2011
ISSN: 0188-7009,1661-4909
DOI: 10.1007/s00006-011-0294-4