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 很少会这么幸运 基子也特征向量。

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

看一下如果基向量恰好特征向量会发生什么。

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

唯一特征值2 但平面上每个向量具有这个特征值特征向量。

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

向量 线性代数核心主题 像行列式和特征向量 似乎与选择坐标系无关。

What we want is a non zero eigenvector.

我们一个非零特征向量。

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.

解释这个方法所有基向量特征向量 这个矩阵对角线元素它们特征值。

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乘以某个值一样。

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一个不稳定基础有关 而不与特征向量和特征值本身有关。

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 关于空间中箭头向量 像点积或者特征向量有直接类似物。