Pfaffian and decomposable numerical range of a complex skew symmetric matrix
نویسندگان
چکیده
منابع مشابه
Pfaffian and Decomposable Numerical Range of a Complex Skew Symmetric Matrix
In the literature it is known that the decomposable numerical range W∧ k (A) of A ∈ Cn×n is not necessarily convex. But it is not known whether W∧ k (A) is star-shaped. We construct a symmetric unitary matrix A ∈ Cn×n such that the decomposable numerical range W∧ k (A) is not star-shaped and hence not simply connected. We then consider a real analog R∧ k (A) and show that R∧ k (A) is star-shape...
متن کاملPfaffian and decomposable numerical range of a complex skew symmetric matrix
In this talk, we discuss the maximum number of n × n pure imaginary quaternionic solutions to the Hurwitz matrix equations given by TiT ∗ j + TjT ∗ i = 2δijI, i, j = 1, . . . , p, where δij is the Kronecker delta. The numerical radius of weighted shift operators Speaker Mao-Ting Chien (Soochow University), [email protected] Co-author Hiroshi Nakazato (Hirosaki University). Abstract Let T be a ...
متن کاملA Range Associated with Skew Symmetric Matrix
We study the range S(A) := {xT Ay : x, y are orthonormal in Rn}, where A is an n×n complex skew symmetric matrix. It is a compact convex set. Power inequality s(A) ≤ s(A), k ∈ N, for the radius s(A) := maxξ∈S(A) |ξ| is proved. When n = 3, 4, 5, 6, relations between S(A) and the classical numerical range and the k-numerical range are given. Axiomatic characterization of S(A) is given. Sharp poin...
متن کاملOn the decomposable numerical range of operators
Let $V$ be an $n$-dimensional complex inner product space. Suppose $H$ is a subgroup of the symmetric group of degree $m$, and $chi :Hrightarrow mathbb{C} $ is an irreducible character (not necessarily linear). Denote by $V_{chi}(H)$ the symmetry class of tensors associated with $H$ and $chi$. Let $K(T)in (V_{chi}(H))$ be the operator induced by $Tin text{End}(V)$. Th...
متن کاملon the decomposable numerical range of operators
let $v$ be an $n$-dimensional complex inner product space. suppose $h$ is a subgroup of the symmetric group of degree $m$, and $chi :hrightarrow mathbb{c} $ is an irreducible character (not necessarily linear). denote by $v_{chi}(h)$ the symmetry class of tensors associated with $h$ and $chi$. let $k(t)in (v_{chi}(h))$ be the operator induced by $tin text{end}(v)$. the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2009
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081080902899077