If P is an orthogonal projection matrix, what is the result of the operation P times P?
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P
Projection matrices are idempotent, meaning applying the projection a second time does not change the result. This reflects the geometric intuition that once a vector is projected onto a subspace, it already lies within that subspace.
Also asked as:
- For an orthogonal projection matrix P, what does P squared (P * P) equal?