منابع مشابه
On the Matrix Equation Xa − Ax = X
We study the matrix equation XA − AX = X p in M n (K) for 1 < p < n. It is shown that every matrix solution X is nilpotent and that the generalized eigenspaces of A are X-invariant. For A being a full Jordan block we describe how to compute all matrix solutions. Combinatorial formulas for A m X ℓ , X ℓ A m and (AX) ℓ are given. The case p = 2 is a special case of the algebraic Riccati equation.
متن کاملA Note on the Normwise Perturbation Theory for the Regular Generalized Eigenproblem Ax = Bx
In this paper, we present a normwise perturbation theory for the regular generalized eigenproblem Ax = Bx, when is a simple and nite eigenvalue, which departs from the classical analysis with the chordal norm 9]. A backward error and a condition number are derived for a choice of exible measure to represent independent perturbations in the matrices A and B. The concept of optimal backward error...
متن کاملA Mesh Refinement Method for Ax = \ Bx
The aim of this paper is to introduce a simple but efficient mesh refinement strategy for use with inverse iteration for finding one or a few solutions of an ordinary or partial differential eigenproblem of the form Ax «■ \Bx. The focus is upon the case where A and B are symmetric and B is positive definite, although the approaches have a very broad application. A discussion of the combined use...
متن کاملGershgorin Theory for the Generalized Eigenvalue Problem Ax — \ Bx
A generalization of Gershgorin's theorem is developed for the eigenvalue problem Ax = XBx and is applied to obtain perturbation bounds for multiple eigenvalues. The results are interpreted in terms of the chordal metric on the Riemann sphere, which is especially convenient for treating infinite eigenvalues.
متن کاملA note on a theorem of Ax
During the Model Theory and Applications to Algebra and Analysis Semester in the Newton Institute in Cambridge (spring 2005), Boris Zilber suggested to look at possible generalizations of 1.1 to the positive characteristic case. Unfortunately, we have not fully succeeded as yet, therefore this note is concerned mostly with characteristic 0 generalizations of 1.1 and only a small discussion abou...
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ژورنال
عنوان ژورنال: The Computer Journal
سال: 1965
ISSN: 0010-4620,1460-2067
DOI: 10.1093/comjnl/8.3.279