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

这是场噩梦 当然可以 你很少会这么幸运 因为你基因子也是特征向。

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

看下如果基向恰好是特征向会发生什么。

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

特征值是2 但是平面上每个向是具有这个特征值特征向。

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

向 代数核心主题 像行列式和特征向 似乎与你选择坐标系无关。

What we want is a non zero eigenvector.

我们要是个非零特征向。

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.

解释这个方法是所有基向是特征向 这个矩阵对角元素是它们特征值。

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.

这个表达式说是矩阵向乘积A乘以V得到结果和特征向V乘以某个值是样。

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是与这些主题中个不稳定基础有关 而不是与特征向和特征值本身有关。

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大部分概念 关于空间中箭头向 像点积或者特征向有直接类似物。