Eigensystem

Eigensystem[m]
给出方阵 m 的特征值和特征向量构成的列表 .

Eigensystem[{m,a}]
给出关于 am 的广义的特征值和特征向量.

Eigensystem[m,k]
给出 m 的前 k 个的特征值和特征向量.

Eigensystem[{m,a},k]
给出前 k 个特征值和特征向量.

更多信息和选项更多信息和选项

  • 如果 m 包含近似实数或复数,Eigensystem 求数值特征值和特征向量.
  • 对于近似数值矩阵 m,特征向量被规范化.
  • For exact or symbolic matrices m, the eigenvectors are not normalized.
  • 所有给出的非零特征值都是线性无关的. 如果特征向量的个数等于非零特征值的个数,则相应特征值和特征向量在相应位置分别用它们的列表给出.
  • 如果特征值比无关的特征向量多,则每个特定的特征值会跟上一个零向量. »
  • 特征值和特征向量满足矩阵方程 m.Transpose[vectors]==Transpose[vectors].DiagonalMatrix[values].  »
  • 广义的有限特征值和特征向量满足 m.Transpose[vectors]==a.Transpose[vectors].DiagonalMatrix[values].
  • 可以用 valsvecs 表示相应的特征值和特征向量. »
  • Eigensystem[m,spec] 等价于应用 Take[,spec]Eigensystem[m] 的每个元素.
  • SparseArray 的对象可用于 Eigensystem 中. »
  • Eigensystem has the following options and settings:
  • CubicsFalsewhether to use radicals to solve cubics
    MethodAutomaticselect a method to use
    QuarticsFalsewhether to use radicals to solve quartics
    ZeroTestAutomatictest for when expressions are zero
  • The ZeroTest option only applies to exact and symbolic matrices.
  • Explicit Method settings for approximate numeric matrices include:
  • "Arnoldi"Arnoldi iterative method for finding a few eigenvalues
    "Banded"direct banded matrix solver
    "Direct"direct method for finding all eigenvalues
    "FEAST"FEAST iterative method for finding eigenvalues in an interval (applies to Hermitian matrices only)
  • The method is also known as a Lanczos method when applied to symmetric or Hermitian matrices.
  • The and methods take suboptions Method->{"name",opt1->val1,}, which can be found in the Method subsection.

范例范例打开所有单元关闭所有单元

基本范例  (4)基本范例  (4)

Eigenvalues and eigenvectors computed with machine precision:

In[3]:=
Click for copyable input
Out[1]=

Eigenvalues and eigenvectors computed with 20-digit arbitrary precision:

In[1]:=
Click for copyable input
Out[1]=

明确的特征值和特征向量:

In[1]:=
Click for copyable input
Out[1]=

Symbolic eigenvalues and eigenvectors:

In[1]:=
Click for copyable input
Out[1]=
1988年引入
(1.0)
| 2014年更新
(10.0)