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

这一场噩梦 当然可以 你很少会这么幸运 因为你的基因子也特征。

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

看一下如果基恰好特征会发生什么。

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

唯一的特征值2 但平面上的每个有这个特征值的特征。

Vectors, core topics in linear algebra, like determinants and eigenvectors, seem indifferent to your choice of coordinate systems.

线性代数的核心主题 像行列式和特征 似乎与你选择的坐标系无关。

What we want is a non zero eigenvector.

我们要的一个非零特征。

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.

解释这个的方法所有的基特征 这个矩阵的对角线元素它们的特征值。

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.

这个表达式说的矩阵乘积A乘以V得到的结果和特征V乘以某个值一样的。

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.

对正交的困惑通常更多的与这些主题中的一个不稳定的基础有关 而不与特征和特征值本身有关。

In fact, most of the concepts I've talked about in this series, with respect to vectors as arrows in space, things like the dot product or eigenvectors have direct analogs.

事实上 我在这个系列中讲过的大部分概念 关于空间中的箭头 像点积或者特征有直接的类似物。