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Let ##v1## and ##v2## be two vectors in an inner product space over ##\mathbb{C}##.

Suppose that ## \langle v1 , v2 \rangle = ||v1|| \cdot ||v2|| ##, i.e. the special case of Cauchy Schwarz when it is an equality. Then prove that ##v1## is a scalar multiple of ##v2##, assuming neither vector is ##0##.

I've tried using the triangle inequality and some other random stuff to no avail. I believe there's some algebra trick involved, could someone help me out? I really want to prove this and get on with my machine learning.

Thanks!

BiP