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, the latter usually used where those objects are straight lines or planes.
Sources
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- 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next): $\text I.2.1$