Just like a few examples where this is used is fraud detection in banks, like some payment events go in, you aggregate feature vectors, some of that through a fraud model.

就像一些使用这个的例子， 在银行中进行检测，比如有些支付事件进来， 你聚合特征向，其中一部分通模型。

A sheer E.G. doesn't have enough eigen vectors to span the full space.

纯粹的E G 没有足够的特征向来张成整个空间。

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.

解释这个的方法是所有的基向都是特征向 这个矩阵的对角线元素是的特征值。

So finding the eigen vectors and their eigen values of the matrix A comes down to finding the values of V and lambda that make this expression true.

所以求出矩阵A的特征向的特征值归结为求出V使这个表达式成立的值。

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

这是一场噩梦 当然可以 你很少会这么幸运 因为你的基因子也是特征向。

The fact that there are no real number solutions indicates that there are no eigen vectors.

没有实数解的事实表明没有特征向。

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

唯一的特征值是2 但是平面上的每个向都是具有这个特征值的特征向。

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.

这个表达式说的是矩阵向乘积A乘以V得到的结果特征向V乘以某个值是一样的。

For those of you wondering why we care about alternate coordinate systems, the next video on eigen vectors and eigen values, we'll give a really important example of this.

对于那些想知道为什么我要关心交替坐标系的人 下一集关于特征向特征值的视频 我会给出一个很重要的例子。

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是与这些主题中的一个不稳定的基础有关 而不是与特征向特征值本身有关。

All of the vectors on the x axis are eigen vectors with eigen valued one, since they remain fixed in place.

x轴上的所有向都是特征值为1的特征向 因为保持固定。

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

看一下如果基向恰好是特征向会发生什么。

What we want is a non zero eigenvector.

我要的是一个非零特征向。