Definition:Birkhoff-James Orthogonality

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

Let $x, y \in V$.

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

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

for all scalars $\lambda$.

This is denoted:

$x \perp_B y$

Source of Name

This entry was named for Garrett Birkhoff and Robert Clarke James.