Determinantal and eigenvalue inequalities for matrices with numerical ranges in a sector
نویسندگان
چکیده
منابع مشابه
Determinantal and Eigenvalue Inequalities for Matrices with Numerical Ranges in a Sector
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...
متن کاملProperties 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...
متن کاملDeterminantal inequalities for positive definite matrices
Let Ai , i = 1, . . . ,m , be positive definite matrices with diagonal blocks A ( j) i , 16 j 6 k , where A ( j) 1 , . . . ,A ( j) m are of the same size for each j . We prove the inequality det( m ∑ i=1 A−1 i ) > det( m ∑ i=1 (A (1) i ) −1) · · ·det( m ∑ i=1 (A (k) i ) −1) and more determinantal inequalities related to positive definite matrices.
متن کاملDeterminantal Inequalities for Block Triangular Matrices
This paper presents some results that complement (2). We believe our results are of new pattern concerning determinantal inequalities. Let us fix some notation. The matrices considered here have entries from the field of complex numbers. X ′,X ,X∗ stand for transpose, (entrywise)conjugate, conjugate transpose of X , respectively. For two n -square Hermitian matrices X ,Y , we write X > Y to mea...
متن کاملHermitian octonion matrices and numerical ranges
Notions of numerical ranges and joint numerical ranges of octonion matrices are introduced. Various properties of hermitian octonion matrices related to eigenvalues and convex cones, such as the convex cone of positive semidefinite matrices, are described. As an application, convexity of joint numerical ranges of 2×2 hermitian matrices is characterized. Another application involves existence of...
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: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.08.040