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.

唯一的特征值是2 但是平面上的每个向量都是具有这个特征值的特征向量。

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

x轴上的所有向量都是特征值为1的特征向量 因为它们保持固定。

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

当然 拉伸和挤压并没有什么特别的 或者说这些特征值恰好是正的。

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

A是表示以V为图标向量的某个变换的矩阵 lambda是一个数字 即对应的特征值。

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量都是特征向量 这个矩阵的对角线元素是它们的特征值。

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。

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。

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 对应的特征值必须是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。