Eigensystem

 Reference: http://reference.wolfram.com/legacy/v4-zh/Built-inFunctions/ListsAndMatrices/MatrixOperations/Eigenvectors.html

 

Usage

• Eigensystem[ m ] 给出由方阵的特征值和特征向量构成的列表 values , vectors

Notes

• 如果 m 包含了近似实复数， Eigensystem会找出数值的特征值和特征向量.

• 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. • Eigensystem[ m , ZeroTest -> test ] 使用 test 来确定表达式是否被假设为0 .缺省设置为 ZeroTest -> Automatic.

• 特征值和特征向量满足矩阵方程 m.Transpose[ vectors ] Transpose[ vectors ].DiagonalMatrix[ values ].

• 参见 Mathematica 全书: 3.7.9节.

• 同时参见: NullSpace, JordanDecomposition, SchurDecomposition, QRDecomposition.

• 相关包: LinearAlgebra`Orthogonalization`, LinearAlgebra`Cholesky`.

Further Examples

These are the eigenvalues of a 2 x 2 matrix.

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These are the eigenvectors of the matrix.

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This lists the eigenvalues and the eigenvectors for the matrix. The eigenvalues are listed first.

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This verifies the result for the first eigenvalue and its corresponding eigenvector.

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Using Eigensystem to diagonalize a matrix 使用来对角化一个矩阵.

Matrices with non-repeated eigenvalues can be diagonalized using Eigensystem. The eigenvalues give the diagonalized form. The columns of the change of basis matrix b are the eigenvectors.

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We check the diagonalization.

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