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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Eigenvalues and Eigenvectors - MIT Mathematics
math.mit.eduP 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.
![[1] Eigenvectors and Eigenvalues - MIT Mathematics](/cache/preview/2/f/b/9/3/8/e/8/thumb-2fb938e8a0f46eb9794ca1d897d86311.jpg)
[1] Eigenvectors and Eigenvalues - MIT Mathematics
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