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

没有解的事表明没有特征向量。

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

x轴上的所有向量都特征值为1的特征向量 因为它们保持固定。

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

纯粹的E G 没有足够的特征向量来张成整个空间。

4.A set of basis vectors, which are also agen vectors, is called, again, reasonably enough, an eigen basis.

一组基向量 也就原向量 再一次 很合理地称为特征基。

5.If you actually try computing the eigen values of a rotation like this, notice what happens.

如果你试着计算像这样旋转的特征值 注意会发生么。

6.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2 但平面上的每个向量都具有这个特征值的特征向量。

7.But if you can find an eigen basis, it makes matrix operations really lovely.

但如果你能找到一个特征基 它就会让运算变得非常可爱。

8.Of course, there's nothing special about stretching versus squishing, or the fact that these eigen values happen to be positive.

当然 拉伸和挤压并没有么特别的 或者说这些特征值恰好正的。

9.A is the matrix representing some transformation with V as the icon vector, and lambda is a number, namely the corresponding eigen value.

A表示以V为图标向量的某个变换的 lambda一个字 即对应的特征值。

10.In the world of functions, though sometimes they go by different names, things like inner product or eigen function.

在函的世界里 虽然有时它们有不同的名字 比如内积或者特征函。

11.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.

解释这个的方法所有的基向量都特征向量 这个的对角线元素它们的特征值。

12.In particular, I suspect that the reason for this is not so much that eigen things are particularly complicated or poorly explained.

特别地 我怀疑这其中的原因并不特征物特别复杂或解释得很差。

13.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A的特征向量和它们的特征值归结为求出V和使这个表达式成立的值。

14.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特征向量在变换过程中保持在自己张成的空间上的向量。

15.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与这些主题中的一个不稳定的基础有关 而不与特征向量和特征值本身有关。

16.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.

对于那些想知道为么我们要关心交替坐标系的人 下一集关于特征向量和特征值的视频 我们会给出一个很重要的例子。

17.In this case, by the way, the corresponding eigen value would have to be one, since rotations never stretcher squish anything, so the length of the vector would remain the same.

顺便说一下 在这种情况下 对应的特征值必须1 因为旋转不会拉伸压扁任何东西 所以向量的长度保持不变。