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Orthogonal Projection of b on the subspace W

Let b be a vector in tex2html_wrap_inline301 and W be a subspace of tex2html_wrap_inline301 spanned by the vectors tex2html_wrap_inline307 . To find orthogonal projection of b onto W denoted by tex2html_wrap_inline313 form a matrix A whose columns are the vectors tex2html_wrap_inline307 then solve the normal s ystem tex2html_wrap_inline273. If x is the solution vector then Ax is the orthogonal projection of b onto W.

Orthogonal Projection or tex2html_wrap_inline301 onto W

Let W be a subspace of tex2html_wrap_inline301 spanned by the basis vectors tex2html_wrap_inline307 . To find orthogonal projection of tex2html_wrap_inline301 onto W denoted by [P] form a matrix A whose columns are the vectors tex2html_wrap_inline307 then transformation tex2html_wrap_inline347 is called the orthogonal projection of tex2html_wrap_inline301 onto W.