I know that to find the projection of an element in R^n on a subspace W, we need to have an orthogonal basis in W, and then applying the formula formula for projections.(adsbygoogle = window.adsbygoogle || []).push({});

However, I don;t understand why we must have an orthogonal basis in W in order to calculate the projection of another vector onto W. Why can't we use just some normal basis in W. Is it to make the computation easier, or is there a deeper reason why we can't find projections without orthogonal bases?

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# I Orthogonal basis to find projection onto a subspace

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