The hat matrix is a projection matrix so it's idempotent. i.e. it only has eigenvalues of 0 or 1.

Dec 24, 2017 · I believe you’re asking for the intuition behind those three properties of the hat matrix, so I’ll try to rely on intuition alone and use as little math and higher level linear algebra concepts as possible. Preliminaries

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Sep 28, 2020 · The matrix $\bf{H}$ is the projection matrix onto the column space of $\bf{X}$. But the first column of $\bf{X}$ is all ones; denote it by $\bf{u}$ . This implies that $\bf{Hu}$ = $\bf{u}$ , because a projection matrix is idempotent.

Hat matrix with simple linear regression. Ask Question Asked 8 years, 5 months ago. Modified 8 years, 5 ...

Hat Matrix Identities in Regression. Ask Question Asked 12 years, 4 months ago. Modified 12 years, 4 ...

Oct 22, 2014 · If we now pass to the Jordan Normal Form $\;J_A\;$ of $\;A\;$ (i.e., in this case the diagonal form of the matrix) , we see that we'll get as many $\;1$ 's on the diagonal as the rank of the matrix, because $\operatorname{rank} J_A = \operatorname{rank} A$, and thus we have that $$\operatorname{Tr} A= \operatorname{Tr} J_A= \operatorname{rank} A$$

Feb 7, 2020 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Oct 26, 2015 · Proof that trace of 'hat' matrix in linear regression is rank of X. 2.

Oct 27, 2018 · Properties of OLS hat matrix from a design matrix whose rows sum to $1$ 0.