How to find orthogonal complement in $\ell_{2}$ to $L = \{x\in\ell_{2},x=(a_{1},a_{2}...):\sum_{k=1}^{n}a_{k} = 0\}$. I just don't know how to approach. I know that this subpace is closed, i.e dense in whole space. I want to find complement without knowing that $L$ is everywhere dense. But i just can't find complement subspace. Any hints?
2026-04-05 09:39:12.1775381952
orthogonal complement in $\ell_{2}$ to subspace
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