Using an independent derivation by Kohn, the full meaning of Kato's formulas for upper and lower bounds to eigenvalues of a Hermitian operator is shown. These bounds are the best possible when the only information available on a particular eigenvalue problem is a suitable trial function and an...
Proof is given that when the Eckart estimate to the overlap integral is used in the Cohen–Feldmann lower bound on the eigenvalue of a Hermitian operator, the only self-consistent bound which can be obtained is that of Temple–Kato. It is pointed out that a similar situation holds for the...
Eigenvalues and eigenfunctionsSome properties and applications of Hermitian operators composed of any integral operator and its adjoint are studied. Such ... Naoki Inagaki,Robert J. Garbacz - 《Antennas & Propagation IEEE Transactions on》 被引量: 46发表: 1982年 Eigenvalues of non-hermitian random ...
The first known use of eigenvalue was in 1927 eigenvalues 例句 1.The procedure described above applies to the eigenvalues and eigenfunctions of any Hermitian operator. 用上述运算方法也能求出任一厄密算符的本征值和本征函数. 2.In math, when you see multiple value solutions, these are eigenvalues....
The authors consider the first order asymptotics, as n→∞, of the extreme eigenvalues of the n×n Hermitian Toeplitz matrices whose first rows have the form [a 0 ,a 1 ,,a n-1 ] where, for some α>0, a k =k α +o(k α ) as k→∞. Following an approach introduced by H. ...
The n roots of this equation A are called theeigenvalues. 这个方程的n根叫做A的特征值. 辞典例句 The procedure described above applies to theeigenvaluesand eigenfunctions of any Hermitian operator. 用上述运算方法也能求出任一厄密算符的本征值和本征函数. ...
Abstract In this chapter we will study inequalities that are used for localising the spectrum of a Hermitian operator. Such results are motivated by several interrelated considerations. It is not always easy to calculate the eigenvalues of an operator. However, in many scientific problems it is eno...
Hermitian matrices have real eigenvalues. The Cauchy interlace theorem states that the eigenvalues of a Hermitian matrix A of order n are interlaced with those of any principal submatrix of order n 1. Theorem 1 (Cauchy Interlace Theorem). Let A be a Hermitian matrix of order n, and let B ...
On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form A + XTX*, originally studied in Marcenko and Pas... JW Silverstein,ZD Bai - 《Journal of Multiv...
We recall relevant properties of its first eigenfunction for finite $p$... M Belloni,Parma,B Kawohl,... - 《Journal of the European Mathematical Society》 被引量: 50发表: 2005年 A vanishing theorem on Kaehler Finsler manifolds Hodge-Laplace operatorHermitian metricLet M be a connected ...