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Question

What does orthogonal projection means?


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Solution

Orthogonal projection:

Let U be a subspace in Rn and x be a vector in Rn. The closest vector of x in U is xU.

Then xU is known as the orthogonal projection of x in U.

Orthogonal projection onto a line:

If L=spanU is a line then

xL=u·ux·uu and xL=x-xL

for any vector x.


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