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Prove the Extended Pythagorean Theorem: E^2=lbl

We've defined the error between a vector b in Euclidean vector space R^m and its projection p onto a subspace of R^m as E=lb-pl. Prove the extended pythagorean Theorem: E^2=lbl^2 - lPl^2.

Solution Summary

An extended Pythagorean theorem is proven.

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