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Search results with tag "Formula for the orthogonal projection"
18.06 Quiz 2 April 7, 2010 Professor Strang
math.mit.eduSolution The general formula for the orthogonal projection onto the column space of a matrix A is P= A(ATA) 1AT: Here, A = 2 6 6 6 4 2 1 3 3 7 7 7 5 so that P = 1 14 2 6 6 6 4 4 2 6 2 1 3 6 3 9 3 7 7 7 5 Remarks: Since we’re projecting onto a one-dimensional space, ATA is just a number and we can write things like P= (AAT)=(ATA). This won’t ...
The formula for the orthogonal projection
www.math.lsa.umich.eduYour textbook states this formula without proof in Section 5.4, so I thought I’d write up the proof. I urge you to also understand the other ways of dealing with orthogonal projec-tion that our book discusses, and not simply memorize the formula. Example Let V be the span of the vectors (1 2 3 4)T and (5 6 7 8)T. These two vectors are linearly