\begin{definition}[Definition:Birkhoff-James Orthogonality]
Let $\struct {V, \norm {\,\cdot\,} }$ be a normed linear space.
Let $x, y \in V$.
Then $x$ and $y$ are '''Birkhoff-James orthogonal''' {{iff}} 
:$\norm {x + \lambda y} \ge \norm y$
for all scalars $\lambda$.
This is denoted:
:$x \perp_B y$
{{NamedforDef|Garrett Birkhoff|name2 = Robert Clarke James|cat = Birkhoff, Garrett|cat2 = James}}
\end{definition}