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  "body": "\n## Statement\n\nLet $V$ be a finite-dimensional inner product space over $\\R$ or $\\C$, and let $W$ be a subspace of $V$.\nThen\n$$(W^\\perp)^\\perp = W,$$\nwhere $W^\\perp$ is the [[orthogonal complement|0XJXTBCB2T]] of $W$.\n\n## Remarks\n\nEach vector of the subspace is orthogonal to each vector of its orthogonal complement, so $W \\subseteq (W^\\perp)^\\perp$. Both have dimension $\\dim V - \\dim W^\\perp = \\dim W$.\nIn an infinite-dimensional Hilbert space, $(W^\\perp)^\\perp$ is the closure of $W$.\n\n## Explanations\n\n### L1 human\n\nTaking the orthogonal complement twice gives back the original subspace.\nThe complement of the complement of a line is the same line.\n",
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