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        "quote": "带有内积的复向量空间将简称为 <u id=\"concept-5-inner-product-space\" class=\"concept-term\" data-concept-identity=\"urn:uuid:556c76cb-7433-4f01-86f1-cbbf0bc6fe95\" data-concept-route=\"/concept-identities#concept-556c76cb-7433-4f01-86f1-cbbf0bc6fe95\">内积空间(inner product space)</u>。如果 $V$ 是有限维的，则常称为有限维 <u id=\"concept-5-hilbert-space\" class=\"concept-term\" data-concept-identity=\"urn:uuid:34c6c0e8-a933-4a51-bbf6-7721075b239c\" data-concept-route=\"/concept-identities#concept-34c6c0e8-a933-4a51-bbf6-7721075b239c\">希尔伯特空间(Hilbert space)</u>，但对于无限维空间，希尔伯特空间这一术语仅适用于该空间是完备的情形（见第 13 章）。",
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