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        "quote": "$\\Omega$ 的这一选择并不像表面上那样任意。对 $\\mathbb R^{2d}$ 上任意反对称的[<u class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/nondegenerate-bilinear-form\" data-concept-identity=\"urn:uuid:f99d2218-e64e-42aa-ac15-b1adf3fb020d\" data-concept-route=\"/concept-identities#concept-f99d2218-e64e-42aa-ac15-b1adf3fb020d\" id=\"first-db368e14c04f50e9d4aa-zh\">非退化双线性形式(non-degenerate bilinear form)</u>](../../../../../concepts/linear-algebra/nondegenerate-bilinear-form)，都能找到一组基，使其具有上面给出的 $\\Omega$ 的形式（证明见[8]）。复化到 $\\mathbb C^{2d}$ 并用同一公式定义 $\\Omega$ 后，这个结论仍成立。实数和复数情形下，保持该形式的群分别记为 $Sp(2d,\\mathbb R)$ 和 $Sp(2d,\\mathbb C)$。",
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