Show that $(y_1, y_2) ^2 = (y_1, y_1) (y_2, y_2)$ iff $y_1$ and $y_2$ are linearly dependent, where $y_1, y_2 \in E$

Question

In the book of Linear Algebra by Werner Greub, at page 285, it is stated in a proof that

Let $E$ be a n-dimensional inner product space.Then $$(y_1, y_2) ^2 = (y_1, y_1) (y_2, y_2)$$ iff $y_1$ and $y_2$ are linearly dependent.

If it clear that $\Leftarrow$ holds, but how do we show $\Rightarrow$ ?

Answer 1

That direction is the equality case of the Cauchy-Schwarz inequality.