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        "quote": "若向量空间 $V$ 可由一个有限集张成，即 $V = L ( A )$ ，其中 $A = \\{ v _ { 1 } , v _ { 2 } , \\ldots , v _ { n } \\}$ ，则称 $V$ 为<u id=\"concept-3-finite-dimensional\" class=\"concept-term\" data-concept-identity=\"urn:uuid:f214d7a0-7106-43ff-bc0a-3801debd64c2\" data-concept-route=\"/concept-identities#concept-f214d7a0-7106-43ff-bc0a-3801debd64c2\">有限维(finite dimensional)</u>的 [7]。否则，称 $V$ 为<u id=\"concept-3-infinite-dimensional\" class=\"concept-term\" data-concept-identity=\"urn:uuid:3ef9fce1-922f-464f-b973-2d43ecaddccd\" data-concept-route=\"/concept-identities#concept-3ef9fce1-922f-464f-b973-2d43ecaddccd\">无限维(infinite dimensional)</u>的。当 $V$ 为有限维时，其<u id=\"concept-3-dimension\" class=\"concept-term\" data-concept-identity=\"urn:uuid:4d8daf81-914a-426c-9cc7-534fc6eed006\" data-concept-route=\"/concept-identities#concept-4d8daf81-914a-426c-9cc7-534fc6eed006\">维数(dimension)</u> $\\dim V$ 定义为使得 $V$ 可由仅由 $n$ 个向量组成的集合张成的最小数目 $n$。",
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