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- Why is the orthogonal projection formula written as ##P_A=A(A^TA)^{-1}A^T## as opposed to ##P_A=(A^T)^{-1}A^T##?
Aren't they the same thing? If so, why would textbooks write the former? Ex: https://textbooks.math.gatech.edu/ila/projections.html or http://www.math.lsa.umich.edu/~speyer/417/OrthoProj.pdf or https://en.wikipedia.org/wiki/Projection_(linear_algebra)#Orthogonal_projections
Thank you!
Thank you!