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。

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。

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。

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是在变换过程中保持在自己张成的空间上的向量。

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。

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。