eigenvector background

eigenvector

/ˈaɪɡənˌvɛktər/ /ˈaɪɡənˌvɛktɔːr/

Illustration eigenvector - Image 1

noun

特征向量

Given a linear transformation T, a vector x such that Ax=\lambda x for some scalar \lambda

Examples :

"When stretching a photograph horizontally, an eigenvector of the transformation could be a vertical line; it remains a vertical line, only changing in length (or possibly direction, if the scaling factor is negative). "

当水平拉伸一张照片时，这种变换的特征向量可能是一条垂直线；它仍然保持为一条垂直线，只是长度发生了改变（或者，如果缩放因子是负数，方向可能也会改变）。

math technical science

Illustration eigenvector - Image 1

noun

特征向量

Specifically, given a matrix A, the eigenvector of the transformation "leftside multiplication by A"

Examples :

"After being multiplied by a specific matrix representing a stretching and rotation, the eigenvector remains pointing in the same direction, only scaled in length. "

被一个代表拉伸和旋转的特定矩阵相乘后，特征向量的方向保持不变，只是长度会发生变化。

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