Given vectors prove that
if and only if and
are orthogonal.
Proof.
From Theorem 13.12(f) (page 483 of Apostol) we know
But if and only if
and
are orthogonal (from the definition of orthogonality). Thus,
if and only if
and
are orthogonal
It took me 20 minutes to realize there was a typo in the formula.
There is a typo in the formula as stated. Instead of adding the squared norms of A and B, you need to multiply them instead