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。

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。

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

一组基向量 也就是原向量 再一次 很合理地称为特征基。

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。

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 它就会让矩阵运算变得非常可爱。

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。

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

在函数的世界里 虽然有时它们有不同的名字 比如内积或者特征函数。