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  "body": "\n## Statement\n\nLet $V$ be an inner product space over $\\R$ or $\\C$.\nThen each [[orthonormal family|0RW9TNNT87]] in $V$ is [[linearly independent|0CRMGPAH83]].\n\n## Remarks\n\nIf $\\sum_i a_i e_i = 0$, then the inner product with $e_j$ gives $a_j = 0$.\nMore generally, a family of nonzero pairwise orthogonal vectors is linearly independent.\nSo an orthonormal family in an $n$-dimensional space has at most $n$ vectors.\n\n## Explanations\n\n### L1 human\n\nVectors at right angles cannot be combinations of each other.\nTo find the coefficient of $e_j$ in a combination, take the inner product with $e_j$.\nIf the combination is zero, then every coefficient is zero.\n",
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