Higher Rank Numerical Hulls of Matrices
نویسندگان
چکیده
For any n×n matrix A , we use the joint higher rank numerical range, Λk(A, . . . ,Am) , to define the higher rank numerical hull of A . We characterize the higher rank numerical hulls of Hermitian matrices. Also, the higher rank numerical hulls of unitary matrices are studied. Mathematics subject classification (2010): 15A60,81P68.
منابع مشابه
On higher rank numerical hulls of normal matrices
In this paper, some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated. A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given. Moreover, using the extreme points of the numerical range, the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$, where $A_1...
متن کاملSome 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 $V^k(A)=sigma(A)$.
متن کاملSome Results on Polynomial Numerical Hulls of Perturbed Matrices
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 کاملF Ur Mathematik in Den Naturwissenschaften Leipzig Quasiconvex Hulls in Symmetric Matrices Quasiconvex Hulls in Symmetric Matrices
We analyze the semiconvex hulls of the subset K in symmetric matrices given by K = fF 2 M 22 : F T = F; jF 11 j = a; jF 12 j = b; jF 22 j = cg that was rst considered by Dacorogna&Tanteri Commun. in PDEs 2001]. We obtain explicit formulae for the polyconvex, the quasiconvex, and the rank-one convex hull for ac ? b 2 0 and show in particular that the quasiconvex and the polyconvex hull are diier...
متن کاملQuasiconvex Hulls in Symmetric Matrices
We analyze the semiconvex hulls of the subset K in symmetric matrices given by K fF M F F jF j a jF j b jF j cg that was rst considered by Dacorogna Tanteri Commun in PDEs We obtain explicit formulae for the polyconvex the quasiconvex and the rank one convex hull for ac b and show in particular that the quasiconvex and the polyconvex hull are di erent if strict inequality holds For ac b we obta...
متن کامل