The projection of a vector which is in a subspace is the vector itself.

Created almost 9 years ago, updated about 8 hours ago

If $v\in W$, then $P_Wv=v$, because $v=v+0$ is its orthogonal decomposition. Therefore every nonzero vector in the image of a projection is an eigenvector with eigenvalue one. Vectors in its kernel have eigenvalue zero.

Parents

Like how this is organised?

Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.