Isospectral-like flows and eigenvalue problem

Authors:
Maria Przybylska
Affiliations:
Toruń Centre for Astronomy, Nicholaus Copernicus University, Gagarina 11, 87-100 Toruń, Poland
Venue:
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
Year:
2003

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Abstract

We show that the Lax equation ?? = [N, L] applied for calculating the eigenvalues of matrices is only one in a whole family of matrix differential equations related to eigenvalue problem. All these equations are built by means of various representations ρ of a Lie algebra g on Kn×n. A general connection between matrix differential equation L = ρN(L) and FG eigenvalue algorithm is shown. Remarks concerning practical applications of this connection to matrix eigenvalues calculations are also presented.