Concave functions of partitioned matrices with numerical ranges in a sector
نویسندگان
چکیده
منابع مشابه
Properties of matrices with numerical ranges in a sector
Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruen...
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Let A = ( A11 A12 A21 A22 ) ∈ Mn, where A11 ∈ Mm with m ≤ n/2, be such that the numerical range of A lies in the set {eiφz ∈ C : |=z| ≤ (<z) tanα}, for some φ ∈ [0, 2π) and α ∈ [0, π/2). We obtain the optimal containment region for the generalized eigenvalue λ satisfying λ ( A11 0 0 A22 ) x = ( 0 A12 A21 0 ) x for some nonzero x ∈ C, and the optimal eigenvalue containment region of the matrix I...
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The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix A ∈ Mn has eigenvalues a1, . . . , an, then its higher rank numerical range Λk(A) is the intersection of convex polygons with vertices aj1 , . . . , ajn−k+1 , where 1 ≤ j1 < · · · < jn−k+1 ≤ n. In this paper, it is shown that ...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2017
ISSN: 1331-4343
DOI: 10.7153/mia-20-40