If we want to caculate the projection of a(adsbygoogle = window.adsbygoogle || []).push({}); singlevector, v=(1,2) (which is an element of an R2 vector space called V) onto the subspace of V (which we call W), do we use

projection of v onto W = <v,w1>w1 + <v,w2>w2 + ........ <v,wn>wn

However, if the individual values of v are not known (that is v=(x,y) ), do we calculate the matrix of projection ?

that is, we do A(A[itex]^{T}[/itex]A)[itex]^{-1}[/itex]A[itex]^{T}[/itex]

If we have to determine the matrix of projection, is it because we don't know what x and y is, so the safe bet is to determine the matrix of projection ?

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# Question about projections and subspaces

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