Linear Algebra and Its Applications · Problem 3.2.21

Orthogonality — Gilbert Strang

Mathematics · cosines-projections-onto-lines

Problem

Compute the projection matrices aaT/aTaaa^T/a^Ta onto the lines through a1=(−1,2,2)a_1 = (-1,2,2) and a2=(2,2,−1)a_2 = (2,2,-1). Multiply those projection matrices and explain why their product P1P2P_1P_2 is what it is.

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