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Scilab manual >> Linear Algebra > spec

spec

呼び出し手順

```evals=spec(A)
[R,diagevals]=spec(A)

evals=spec(A,B)
[alpha,beta]=spec(A,B)
[alpha,beta,Z]=spec(A,B)
[alpha,beta,Q,Z]=spec(A,B)```

パラメータ

A

B

`A`と同じ次元の実数または複素正方行列

evals

diagevals

alpha

beta

R

L

R

説明

evals=spec(A)

ベクトル`evals` に固有値を返します.

[R,diagevals] =spec(A)

evals=spec(A,B)

[alpha,beta] = spec(A,B)

[alpha,beta,R] = spec(A,B)

[al,be,L,R] = spec(A,B)

[al,be,Z] = spec(A,E)

[al,be,Q,Z] = spec(A,E)

参照

• 行列が対称でない場合, DGEEV および ZGEEV.

• 行列が対称の場合, DSYEV および ZHEEV.

ペンシル固有値計算は Lapack ルーチン DGGEV および ZGGEVに基づいています.

実数および複素行列

• 実数 A 行列

• 対称

固有値と固有ベクトルは実数.

• 非対称

固有値と固有ベクトルは複素数.

• 複素 A 行列

• 対称

固有値は実数だが固有ベクトルは複素数.

• 非対称

固有値,固有ベクトルは複素数.

例

```// MATRIX EIGENVALUES
A=diag([1,2,3]);
X=rand(3,3);
A=inv(X)*A*X;
spec(A)

x=poly(0,'x');
pol=det(x*eye()-A)
roots(pol)

[S,X]=bdiag(A);
clean(inv(X)*A*X)

// PENCIL EIGENVALUES
A=rand(3,3);
[al,be,R] = spec(A,eye(A));
al./be
clean(inv(R)*A*R)  //displaying the eigenvalues (generic matrix)
A=A+%i*rand(A);
E=rand(A);
roots(det(A-%s*E))   //complex case```

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