Definition:Birkhoff-James Orthogonality

Definition
Let $\struct {V, \norm {\,\cdot\,} }$ be a normed linear space.

Let $x, y \in V$.

Then $x$ and $y$ are Birkhoff-James orthogonal


 * $\norm {x + \lambda y} \ge \norm y$

for all scalars $\lambda$.

This is denoted:
 * $x \perp_B y$