What we want is a non zero eigenvector.

我们要是一个非零特征向量。

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

没有实数解事实表明没有特征向量。

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 但是平面上每个向量都是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 似乎与你选择关。

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。

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

x轴上所有向量都是特征值为1特征向量 因为它们保持固定。

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

纯粹E G 没有足够特征向量来张成整个空间。

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 因为你基因子也是特征向量。

The determinant tells you how much a transformation scales areas and eigen vectors are the ones that stay on their own span during a transformation.

行列式告诉你变换对面积缩放程度特征向量是在变换过程中保持在自己张成空间上向量。

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.

解释这个方法是所有基向量都是特征向量 这个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.

这个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乘以某个值是一样。

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特征向量和它们特征值归结为求出V和使这个表达式成立值。

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个不稳定基础有关 而不是与特征向量和特征值本身有关。

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们要关心交替人 下一集关于特征向量和特征值视频 我们会给出一个很重要例子。

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都有直接类似物。