有谁可以介绍一下下， 什么是projection matrix （投影矩阵），以及它的性质？ 关注者 70 被浏览

Nov 24, 2023 · Yes, because any projection matrix $A$, i.e., with $A^2=A$ is conjugated to a block matrix with identity matrix of size $r$ and a zero block. Hence $trace (A)=r=rank (A)$.

Dec 17, 2017 · represent the projection matrix in the plane with respect to the canonical basis. Suppose now we want find the projection matrix from the base $\mathcal {B}$ to the canonical …

I am looking for an intuitive reason for a projection matrix of an orthogonal projection to be symmetric. The algebraic proof is straightforward yet somewhat unsatisfactory. Take for …

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If you can figure out which matrix that is, it's obvious that its inverse is again a projection matrix.

Dec 4, 2018 · How to find Projection matrix onto the subspace Ask Question Asked 7 years, 8 months ago Modified 2 years, 5 months ago

Thanks. What is the intuition behind that i.e. how do you derive that formulation for the projection matrix?

0 You can find the matrix associated with the the transformation projection. The matrix is singular which implies the projection is not invertible.

I understand that the trace of the projection matrix (also known as the "hat" matrix) X*Inv (X'X)*X' in linear regression is equal to the rank of X. How can we prove that from first principles, i.e.