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LinearAlgebra[CharacteristicPolynomial] - 行列の固有多項式の作成
使い方
CharacteristicPolynomial(A, lambda)
パラメータ
A - 行列 lambda - 名前; 変数として使用
説明
CharacteristicPolynomial(A, lambda) 関数は行列 A の固有値を根として持つ lambda の を返します (すべての重複根を考慮します)。
この多項式は lambda*I - A の行列式です、ただし I は dimension(A) の単位行列です。
この関数は LinearAlgebra パッケージの一部ですから、コマンド with(LinearAlgebra) を実行した後にのみ CharacteristicPolynomial(..) の形で使うことができます。ただし、長い形の名前 LinearAlgebra[CharacteristicPolynomial](..) を使えばいつでもアクセスすることができます。
例
with(LinearAlgebra): M := <<1,0,0>|<1,1,0>|<0,3,2>>;
CharacteristicPolynomial(M,x);
solve(%,x);
Eigenvalues(M,output='list');
参照
Matrix, LinearAlgebra[CharacteristicMatrix], LinearAlgebra[MinimalPolynomial], LinearAlgebra[IdentityMatrix], LinearAlgebra[Eigenvalues]
リファレンス
Abdeljaoued, J. "The Berkowitz Algorithm, Maple and Computing the Characteristic Polynomial in an Arbitrary Commutative Ring." MapleTech Vol. 4 No. 3 (Birkhauser, 1997), pp. 21-32
De Boor, C. "An Empty Exercise." ACM SIGNUM Newsletter 25 (1990).
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