Eigenvalues and Eigenvectors - MIT Mathematics
P is symmetric, so its eigenvectors .1;1/ and .1; 1/ are perpendicular. The only eigenvalues of a projection matrix are 0 and 1. The eigenvectors for D 0 (which means Px D 0x/ fill up the nullspace. The eigenvectors for D 1 (which means Px D x/ fill up the column space. The nullspace is projected to zero. The column space projects onto itself.
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