And the way to interpret this is that all the basis vectors are eigenvectors, with the diagonal entries of this matrix being their eigen values.

解释这个方法所有向量都特征向量 这个矩阵对角线元素它们特征值。

It's a nightmare. Of course. You'll rarely be so lucky as to have your basis factors also be eigenvectors.

这噩梦 当然可以 你很会这么幸运 为你子也特征向量。

The only eigen value is two, but every vector in the plane gets to be an eigenvector with that eigen value.

唯特征值2 但平面上每个向量都具有这个特征值特征向量。

What this expression is saying is that the matrix vector product A times V gives the same result as just scaling the eigenvector V by some value lambda.

这个表达式说矩阵向量乘积A乘以V得到结果和特征向量V乘以某个值样。

Confusion about agon stuffs usually has more to do with the shaky foundation in one of these topics than it does with eigenvectors and eigen values themselves.

对正交困惑通常更多与这些主题中个不稳定础有关 而不与特征向量和特征值本身有关。

Take a look at what happens if our basis vectors just so happened to be eigenvectors, e.g.

看下如果向量恰好特征向量会发生什么。

What we want is a non zero eigenvector.

我们要个非零特征向量。