ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation 0
Let $x \in \mathbb{R}^{N \times 1}$ be a D5200: Real column matrix.
Then \begin{equation} x^Tx = \Vert x \Vert_2 \Vert x \Vert_2 = \Vert x \Vert_2^2 \end{equation}
Proofs
Proof 0
Let $x \in \mathbb{R}^{N \times 1}$ be a D5200: Real column matrix.
This result is a particular case of R5192: Cauchy-Schwarz inequality for two real sequences. $\square$