What we want is a non zero eigenvector.

我们要的是一个非零征。

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征。

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 你的基子也是征。

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

一下如果基恰好是征会发生什么。

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

纯粹的E G 没有足够的征来张成整个空间。

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

x轴上的所有都是征值1的征 它们保持固定。

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

唯一的征值是2 但是平面上的每个都是具有这个征值的征。

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

线性代数的核心主题 像行列式和征 似乎与你选择的坐标系无关。

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都是征 这个矩阵的对角线元素是它们的征值。

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.

这个表达式说的是矩阵乘积A乘以V得到的结果和征V乘以某个值是一样的。

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的征和它们的征值归结求出V和使这个表达式成立的值。

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的缩放程度征是在变换过程中保持在自己张成的空间上的。

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 而不是与征和征值本身有关。

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的大部分概念 关于空间中的箭头 像点积或者征都有直接的类似物。

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.

对于那些想知道什么我们要关心交替坐标系的人 下一集关于征和征值的视频 我们会给出一个很重要的例子。