"linearly independent" meaning in English

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "linearly independent (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Estonian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Finnish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with French translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Russian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Spanish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Swedish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Linear algebra",
          "orig": "en:Linear algebra",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "(Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero"
      ],
      "id": "en-linearly_independent-en-adj-rMPGOlMw",
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "vector",
          "vector"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "linear combination",
          "linear combination"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) (Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero"
      ],
      "related": [
        {
          "word": "linear independence"
        }
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "et",
          "lang": "Estonian",
          "sense": "linear algebra",
          "word": "lineaarselt sõltumatu"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "linear algebra",
          "word": "lineaarisesti riippumaton"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "linear algebra",
          "word": "vapaa"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "linear algebra",
          "word": "linéairement indépendant"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "linéjno nezavísimyj",
          "sense": "linear algebra",
          "word": "лине́йно незави́симый"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "linear algebra",
          "word": "linealmente independiente"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "linear algebra",
          "word": "linjärt oberoende"
        }
      ]
    }
  ],
  "word": "linearly independent"
}

{
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "linearly independent (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "related": [
    {
      "word": "linear independence"
    }
  ],
  "senses": [
    {
      "categories": [
        "English adjectives",
        "English adverb-adjective phrases",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English uncomparable adjectives",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Estonian translations",
        "Terms with Finnish translations",
        "Terms with French translations",
        "Terms with Russian translations",
        "Terms with Spanish translations",
        "Terms with Swedish translations",
        "en:Linear algebra"
      ],
      "glosses": [
        "(Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero"
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "vector",
          "vector"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "linear combination",
          "linear combination"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) (Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "et",
      "lang": "Estonian",
      "sense": "linear algebra",
      "word": "lineaarselt sõltumatu"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "linear algebra",
      "word": "lineaarisesti riippumaton"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "linear algebra",
      "word": "vapaa"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "linear algebra",
      "word": "linéairement indépendant"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "linéjno nezavísimyj",
      "sense": "linear algebra",
      "word": "лине́йно незави́симый"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "linear algebra",
      "word": "linealmente independiente"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "linear algebra",
      "word": "linjärt oberoende"
    }
  ],
  "word": "linearly independent"
}