Eigenvalue Problems for Real Nonsymmetric Matrices by Applying Homotopy method

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  • Suzuki Tomohiro
    Dep. of Elec. Eng. & Comp. Sci., Faculty of Engineering, Yamanashi Univ.

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  • ホモトピー法を適用した実数非対称行列の固有値問題
  • ホモトピーホウ オ テキヨウシタ ジッスウ ヒタイショウ ギョウレツ ノ コユ

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Abstract

By applying the homotopy method, the eigenvalue problem for real nonsymmetric matrices reduces to the problem of tracing algebraic curves which are called eigenpaths. Since a real nonsymmetric metrices generally has complex eigenvalues, the eigenpath transitions from the real space to the complex space or vice versa. This bifurcation phenomenon occurs at the point which is called a bifurcation point. The purpose of this paper is to clear that the relation between the bifurcation phenomenon and the multiplicity of eigenvalues. The common bifurcation phenomenon occurs at the point which has an eigenvalue such that algebraic multiplicity is 2 and geometric multiplicity is 1.

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