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-   -   The projection of a vector over the orthogonal subspace of other. (http://mymathforum.com/linear-algebra/344013-projection-vector-over-orthogonal-subspace-other.html)

 coltson April 15th, 2018 07:46 AM

The projection of a vector over the orthogonal subspace of other.

Hello I have the vector B = (2,4,1) and want to project it over the orthogonal subspace of another vector, the vector A = (1,1-1).

I did:
(1,1,-1).(2,4,-1) * (1,1,-1) = \$\displaystyle 7/3 * (1,1,-1) = (7/3,7/3,-7/3)\$
(1,1,-1).(1,1-1)

and then :
\$\displaystyle (7/3,7/3,-7/3) - (2,4,1) = (7/3,7/3,-7/3) - (6/3,12/3,3/3) = (1/3,-5/3,-10/3)\$

Nonetheless, the correct answer it is: \$\displaystyle (1/3,7/3,8/3)\$. So what I am doing wrong? Thanks for the input.

 mathman April 15th, 2018 01:15 PM

Your first calculation has an error. You used (2,4,-1) instead of (2,4,1). If you do it correctly, you will get the correct answer with a minus sign. This is because your final subtraction is opposite the usual definition.

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