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轴上所有向量都是征值为1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.

组基向量 也就是原向量 再次 很合理地称为征基。

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征值 发生么。

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

唯征值是2 但是平面上每个向量都是具有这个征值征向量。

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

但如果你能找到个征基 它就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 拉伸和挤压并没有么别 或者说这些征值恰好是正。

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为图标向量某个变换矩阵 lambda是个数字 即对应征值。

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

在函数世界里 虽然有时它们有不同名字 比如内积或者征函数。

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征向量 这个矩阵对角线元素是它们征值。

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

别地 我怀疑这其中原因并不是征物别复杂或解释得很差。

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征向量和它们征值归结为求出V和使这个表达式成立值。

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缩放程度征向量是在变换过程中保持在自己张成空间上向量。

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个不稳定基础有关 而不是与征向量和征值本身有关。

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.

对于那些想知道为么我们要关心交替坐标系人 下集关于征向量和征值视频 我们给出个很重要例子。

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.

顺便说下 在这种情况下 对应征值必须是1 因为旋转不拉伸压扁任何东西 所以向量长度保持不变。