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

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2017年12月24日 · 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

2018年7月3日 · Perhaps I’m misinterpreting the meaning of $ \beta $ but if $ X^T$ has dimension $ 1 \times p $ and $\beta$ has dimension $ p \times K $, then $\hat{Y} $ would have dimension $1\times K$ and would be a row vector.

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Hat Matrix Identities in Regression. Ask Question Asked 12 years, 2 months ago. Modified 12 years, 2 ...

2015年6月15日 · $\begingroup$ I'll second Ross's comment: I have always seen the hat used to denote a unit vector. Sometimes $\vec x$ is a vector of arbitrary length and $\hat x$ a unit vector; sometimes $\mathbf x$ is an arbitrary vector and $\hat{\mathbf x}$ is a unit vector; but never is a hat placed on a vector that is not of unit length. $\endgroup$ –

2016年12月4日 · Hat Matrix Leverages and Subspaces. Ask Question Asked 8 years, 1 month ago. Modified 8 years, 1 month ago.

2015年6月2日 · Yet, the comment I answered to did miss the meaning of the $\hat{}$ in the linked video (if you watch it, you'll notice that vectors are denoted with an arrow, and that the hat is specifically for unit vectors). $\endgroup$