Hilbert matrixNormKorenblum spaceBERGMANIn this paper, the norm representation of the Hilbert matrix operator H on the Korenblum space H-alpha(infinity) is given for 0 < alpha < 1. In particular, we find an exact value alpha(0) in (0, 1) such that the norm of H is equal to pi/...
Using this norm, we can define the operator norm of a matrix A∈M, which is acting on V. Definition 10.4 Let A∈Mm×n⊂M. Then the operator norm of A is defined as (10.19)‖A‖V:=sup0≠x∈V‖A⋉→x‖V‖x‖V.
norm, which is the maximum of the absolute values of the coefficients. Keep in mind that the lpNorm function applied to a matrix treat the matrix as a vector, and does not return the operator norm of the matrix. Also, I'm new to Eigen, but I imagine that implementing a matrixNorm<in...
The estimator is shown to be consistent in operator norm, when, for instance, we have $p\asymp n$ as n →∞. In other words the largest singular value of the difference between the estimator and the population covariance matrix goes to zero. This implies consistency of all the eigenvalues...
Limiting Case of the Sobolev Inequality in BMO,with Application to the Euler Equations We shall prove a logarithmic Sobolev inequality by means of the BMO-norm in the critical exponents. As an application, we shall establish a blow-up criteri... H Kozono,Y Taniuchi - 《Communications in ...
of vectors or the “angles” between them. The invariance of the norm of a state vector means that the vector’s components can be interpreted as probability amplitudes in both the initial and transformed functions. Therefore, the operation of a unitary operator describes the development of a qu...
Zhang (2015) have proved inequalities on the spectral radius and the operator norm of Hadamard products and ordinary matrix products of finite and infinite non-negative matrices that define operators on sequence spaces. In the current paper we extend and refine several of these results and also ...
2) lp-operator norm lp-算子范数 1. It is then use the lp-operator norm((1≤p≤∞) to obtain two extend inequalities in the variation for general matrix function. 本文用lp-算子范数(1≤p≤∞)的性质证明了一般矩阵函数变差的两个不等式。3) norm of operator 算子的范数 例句>> ...
Also, we prove a numerical radius equality for a $5imes5$ tridiagonal operator matrix.关键词: Norm equality Norm inequality Operator matrix Hankel operator matrix Weakly unitarily invariant norm Spectral radius Numerical radius Usual operator norm Schatten p-norm ...
We describe properties of a Hermitian square matrix M in M_n(C) equivalent to that of having minimal quotient norm in the following sense: ||M|| <= ||M+D|| for all real diagonal matrices D in M_n(C) and || || the operator norm. These matrices are related to some particular ...