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

这是一场 然可以 你很少会这么幸运 因为你基因子也是特征向量。

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是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.

唯一特征值是2 但是平面上每向量是具有这特征值特征向量。

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 似乎与你选择坐标系无关。

What we want is a non zero eigenvector.

我们要是一非零特征向量。

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.

解释这法是所有基向量是特征向量 这矩阵对角线元素是它们特征值。

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.

这表达式说是矩阵向量乘积A乘以V得到结果和特征向量V乘以某值是一样。

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是与这些主题中一不稳定基础有关 而不是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。