Definition:Orthogonal Subspaces

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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.


Sources