Matlab VS Python-eig(A，B)VS sc.linalg.eig(A，B) [英] Matlab VS Python - eig(A,B) VS sc.linalg.eig(A,B)

问题描述

我有以下矩阵sigma和sigmad:

I have the following matrices sigma and sigmad:

sigma:

    1.9958   0.7250
    0.7250   1.3167

已签名:

    4.8889   1.1944
    1.1944   4.2361

如果我尝试解决python中的广义特征值问题，我将获得:

If I try to solve the generalized eigenvalue problem in python I obtain:

    d,V = sc.linalg.eig(matrix(sigmad),matrix(sigma))

V:

    -1     -0.5614
    -0.4352    1

如果我尝试解决g. e.我得到的matlab中的问题:

If I try to solve the g. e. problem in matlab I obtain:

    [V,d]=eig(sigmad,sigma)

V:

    -0.5897    -0.5278
    -0.2564    0.9400

但是d确实是巧合.

推荐答案

特征向量的任何(非零)标量倍数也将是特征向量；只有方向是有意义的，而不是整体规范化.不同的例程使用不同的约定-通常您会看到幅度设置为1或最大值设置为1或-1-某些例程甚至由于性能原因而没有内部一致性.您的两个不同结果是彼此的倍数:

Any (nonzero) scalar multiple of an eigenvector will also be an eigenvector; only the direction is meaningful, not the overall normalization. Different routines use different conventions -- often you'll see the magnitude set to 1, or the maximum value set to 1 or -1 -- and some routines don't even bother being internally consistent for performance reasons. Your two different results are multiples of each other:

In [227]: sc = array([[-1., -0.5614], [-0.4352,  1.    ]])

In [228]: ml = array([[-.5897, -0.5278], [-0.2564, 0.94]])

In [229]: sc/ml
Out[229]: 
array([[ 1.69577751,  1.06366048],
       [ 1.69734789,  1.06382979]])

，因此它们实际上是相同的特征向量.将矩阵视为改变矢量的算子:特征向量是特殊方向，指向该方向的矢量不会被矩阵扭曲，特征值是测量矩阵扩展或收缩向量的因子.

and so they're actually the same eigenvectors. Think of the matrix as an operator which changes a vector: the eigenvectors are the special directions where a vector pointing that way won't be twisted by the matrix, and the eigenvalues are the factors measuring how much the matrix expands or contracts the vector.

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