# Definition:Orthogonal Subspaces

## Definition

Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space.

Let $A$ and $B$ be closed linear subspaces of $V$.

Let $A$ and $B$ be orthogonal in $V$.

Then we say that $A$ and $B$ are orthogonal subspaces.

## Also known as

Two objects that are orthogonal are often seen described as perpendicular.

However, this is usually seen in the context of geometry, where those objects are straight lines.