ThmDex – An index of mathematical definitions, results, and conjectures.

F12428

Formulation 1

Let $x, y \in [0, \infty)^{N \times 1}$ each be an D6043: Unsigned real column matrix.

Then

(1)	\begin{equation} x^T y \leq \Vert x \Vert_2 \Vert y \Vert_2 \end{equation}
(2)	\begin{equation} x^T y = \Vert x \Vert_2 \Vert y \Vert_2 \quad \iff \quad x \text{ and } y \text{ are linearly dependent} \end{equation}