Say that we have $W$, which is a subspace of $\mathbb{R}^n$. Would $W$ and $W^⊥$ have any vectors in common?
2026-05-15 10:43:10.1778841790
Common vectors of a matrix and its orthogonal compliment
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$W$ and $W^{\perp}$ only have the zero in common, because if $y\in W\cap W^{\perp}$, then $y$ is orthogonal to itself.