"linear independence" meaning in English

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  "lang_code": "en",
  "pos": "noun",
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          "text": "The linear independence of a set of vectors can be determined by calculating the Gram determinant of those vectors; if their Gram determinant is zero, then they are linearly dependent, and if their Gram determinant is non-zero, then they are linearly independent. Incidentally, the same Gram determinant can be used to calculate the hyper-volume of a hyper-parallelepiped (whose edges which \"radiate\" from an \"origin\" vertex are described by the vectors).",
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      "glosses": [
        "the state of being linearly independent"
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          "linearly independent",
          "linearly independent"
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        "(algebra) the state of being linearly independent"
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      "translations": [
        {
          "code": "da",
          "lang": "Danish",
          "sense": "state of being linearly independent",
          "tags": [
            "common-gender"
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          "word": "lineær uafhængighed"
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        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "state of being linearly independent",
          "tags": [
            "feminine"
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          "word": "independência linear"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "state of being linearly independent",
          "tags": [
            "feminine"
          ],
          "word": "independencia lineal"
        }
      ]
    }
  ],
  "word": "linear independence"
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          "text": "The linear independence of a set of vectors can be determined by calculating the Gram determinant of those vectors; if their Gram determinant is zero, then they are linearly dependent, and if their Gram determinant is non-zero, then they are linearly independent. Incidentally, the same Gram determinant can be used to calculate the hyper-volume of a hyper-parallelepiped (whose edges which \"radiate\" from an \"origin\" vertex are described by the vectors).",
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      ],
      "glosses": [
        "the state of being linearly independent"
      ],
      "links": [
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          "algebra",
          "algebra"
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        [
          "linearly independent",
          "linearly independent"
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        "(algebra) the state of being linearly independent"
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  "translations": [
    {
      "code": "da",
      "lang": "Danish",
      "sense": "state of being linearly independent",
      "tags": [
        "common-gender"
      ],
      "word": "lineær uafhængighed"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "state of being linearly independent",
      "tags": [
        "feminine"
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      "word": "independência linear"
    },
    {
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      "sense": "state of being linearly independent",
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        "feminine"
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      "word": "independencia lineal"
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  "word": "linear independence"
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