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I just ran over this result: I have a projection (given by the matrix $P = X(X'X)^{-1}X'$ where $X$ is some matrix with full rank) and certain matrix multiplication (with an arbitrary $X$ matrix) yielded $Pw = w$ for $w = $ vector of ones, $w = $ vector with numbers from 1 to matchingdimension, and some other $w$ I tried in Matlab. I doubt that these observations are due to numerical issues. Sadly, I lack knowledge in linear algebra to explain these results.

So my question is: what is the explanation to this result?

Best regards

Syd Amerikaner
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1 Answers1

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$P$ is the projection onto the columns of $X$. If you see $Pw=w$, that means $w$ is in the column space of $X$.

angryavian
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