منابع مشابه
Numerical radius and zero pattern of matrices
Let A be an n n complex matrix and r be the maximum size of its principal submatrices with no o¤-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting kAk be the Frobenius norm of A; we show that jhAx;xij (1 1=2r 1=2n) kAk : This inequality is tight within an additive term O n 2 : If the matrix A is Hermitian, then jhAx;xij (1 1=r) kAk : This inequality...
متن کاملSome numerical radius inequalities with positive definite functions
Using several examples of positive definite functions, some inequalities for the numerical radius of matrices are investigated. Also, some open problems are stated.
متن کاملSpectral radius, symmetric and positive matrices
If ρ(A) > 1, then lim n→∞ ‖A‖ =∞. Proof. Recall that A = CJC−1 for a matrix J in Jordan normal form and regular C, and that A = CJnC−1. If ρ(A) = ρ(J) < 1, then J converges to the 0 matrix, and thus A converges to the zero matrix as well. If ρ(A) > 1, then J has a diagonal entry (J)ii = λ n for an eigenvalue λ such that |λ| > 1, and if v is the i-th column of C and v′ the i-th row of C−1, then ...
متن کاملLinear Maps Preserving Numerical Radius of Tensor Products of Matrices
Let m,n ≥ 2 be positive integers. Denote by Mm the set of m×m complex matrices and by w(X) the numerical radius of a square matrix X. Motivated by the study of operations on bipartite systems of quantum states, we show that a linear map φ : Mmn →Mmn satisfies w(φ(A⊗B)) = w(A⊗B) for all A ∈Mm and B ∈Mn if and only if there is a unitary matrix U ∈Mmn and a complex unit ξ such that φ(A⊗B) = ξU(φ1(...
متن کاملSchur product of matrices and numerical radius (range) preserving maps
Let F (A) be the numerical range or the numerical radius of a square matrix A. Denote by A◦B the Schur product of two matrices A and B. Characterizations are given for mappings on square matrices satisfying F (A ◦ B) = F (φ(A) ◦ φ(B)) for all matrices A and B. Analogous results are obtained for mappings on Hermitian matrices. 2000 Mathematics Subject Classification. 15A04, 15A18, 15A60
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 Algebra and its Applications
سال: 1975
ISSN: 0024-3795
DOI: 10.1016/0024-3795(75)90042-7