Almost Diagonal Matrices with Multiple or Close Eigenvalues
نویسنده
چکیده
If A =D+E where D is the matrix of diagonal elements of A , then when A has some multiple or very close eigenvalues E has certain characteristic properties. These properties are considered both for hermitian and nonhermitian A . The properties are important in connexion with several algorithms for diagonalizing matrices by similarity transformations. *Mathematics Division, National Physical Laboratory, Teddington, Middlesex, England, and Computer Science Department, Stanford University. This work was supported by N.S.F. and O.N.R.
منابع مشابه
A mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...
متن کاملOn Tridiagonalizing and Diagonalizing Symmetric Matrices with Repeated Eigenvalues
We describe a divide-and-conquer tridiagonalizationapproach for matrices with repeated eigenvalues. Our algorithmhinges on the fact that, under easily constructivelyveriiable conditions,a symmetricmatrix with bandwidth b and k distinct eigenvalues must be block diagonal with diagonal blocks of size at most bk. A slight modiication of the usual orthogonal band-reduction algorithm allows us to re...
متن کاملOn 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 Marčenko and Pastur [4], is presented. Here, X (N×n), T (n×n), and A (N×N) are independent, with X containing i.i.d. entries having finite second moments, T is diagonal with real (diagonal) entries, A is Hermitian, and n/N → c > 0 as N → ∞. Under addtional ass...
متن کاملON THE FUNCTION OF BLOCK ANTI DIAGONAL MATRICES AND ITS APPLICATION
The matrix functions appear in several applications in engineering and sciences. The computation of these functions almost involved complicated theory. Thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. The aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. More...
متن کاملEla the Eigenvalue Distribution of Schur Complements of Nonstrictly Diagonally Dominant Matrices and General H−matrices∗
The paper studies the eigenvalue distribution of Schur complements of some special matrices, including nonstrictly diagonally dominant matrices and general H−matrices. Zhang, Xu, and Li [Theorem 4.1, The eigenvalue distribution on Schur complements of H-matrices. Linear Algebra Appl., 422:250–264, 2007] gave a condition for an n×n diagonally dominant matrix A to have |JR+(A)| eigenvalues with p...
متن کامل