Geometric interpretation of “feature space”


Geometric interpretation of “characteristic space”_ Beep beep beep_ bilibili




1.xAll vectors on the axis are the eigenvectors of matrix A. after being acted by a, they are magnified twice.

2.xThe axis is a one-dimensional space.The basis of this one-dimensional space can be a vector (1,0).

3. There are many, many, many eigenvectors corresponding to eigenvalue 2…, A space composed of so many eigenvectors is calledFeature space. This feature space is a space formed by the basis vector (1,0). Similarly, the eigenvalue 3 also corresponds to a feature space, which is a space expanded by the base vector (0,1).

4. The linear combination of eigenvectors corresponding to an eigenvalue is also an eigenvector.