Abstract
In this paper I shall consider the following problem: Given a symmetric (or Hermitian) matrix, find its eigenvalues. I shall use the theory of ordinary differential equations to solve this problem. In particular, I shall describe a spectrum-preserving dynamical system on symmetric (or Hermitian) matrices that flows “downhill” toward diagonal matrices. I shall show that diagonal matrices are the only stable equilibrium points of this flow.
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© 1986 Birkhäuser Verlag Basel
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Driessel, K.R. (1986). On Isospectral Gradient Flows — Solving Matrix Eigenprdblems using Differential Equations. In: Cannon, J.R., Hornung, U. (eds) Inverse Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 77. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7014-6_5
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DOI: https://doi.org/10.1007/978-3-0348-7014-6_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7016-0
Online ISBN: 978-3-0348-7014-6
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