Symbolic Computation of Eigenvalues, Eigenvectors and Generalized Eigenvectors of Matrices by Computer Algebra

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  • 行列の固有値・固有ベクトル・一般固有ベクトルの数式処理による記号的計算法
  • ギョウレツ ノ コユウチ コユウ ベクトル イッパン コユウ ベクトル ノ スウシキ ショリ ニ ヨル キゴウテキ ケイサンホウ

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Abstract

We propose a symbolic formulation for computing eigenvalues, eigenvectors and generalized eigenvectors of rational matrices. Based on the Frobenius normal forms of matrices, our formulation constructs the eigenvectors without solving a system of linear equations by Gaussian elimination over an algebraic extension field. The experimental results show that our algorithm is more efficient than a conventional method implemented on the existing computer algebra systems. Although both Reduce and Maple failed for middle-sized matrices because of the memory problem, our program succeeded in solving the eigenproblem for much larger matrices.

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