Definition:Orthogonal Subspaces

From ProofWiki
Jump to navigation Jump to search

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, the latter usually used where those objects are straight lines or planes.


Sources