"一次独立" meaning in 日本語

{
  "antonyms": [
    {
      "word": "一次従属"
    },
    {
      "word": "線形従属"
    },
    {
      "word": "線型従属"
    }
  ],
  "categories": [
    {
      "kind": "other",
      "name": "日本語",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "日本語 名詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "日本語 形容動詞",
      "parents": [],
      "source": "w"
    }
  ],
  "forms": [
    {
      "form": "いちじどくりつ"
    }
  ],
  "lang": "日本語",
  "lang_code": "ja",
  "pos": "noun",
  "pos_title": "名詞",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "日本語 線型代数学",
          "parents": [],
          "source": "w"
        }
      ],
      "glosses": [
        "ベクトルの一次結合において、全てのスカラーが零であるときのみ、その一次結合がゼロベクトルとなること。a₁v₁ + a₂v₂ + ... + aₖvₖ = 0 であれば、a₁ = a₂ = ... = aₖ = 0 であること。"
      ],
      "id": "ja-一次独立-ja-noun-aqqsFsIq",
      "topics": [
        "linear algebra"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "線形独立"
    },
    {
      "word": "線型独立"
    }
  ],
  "translations": [
    {
      "lang": "英語",
      "lang_code": "en",
      "word": "linear independence"
    },
    {
      "lang": "英語",
      "lang_code": "en",
      "word": "linearly independent"
    }
  ],
  "word": "一次独立"
}

{
  "antonyms": [
    {
      "word": "一次従属"
    },
    {
      "word": "線形従属"
    },
    {
      "word": "線型従属"
    }
  ],
  "categories": [
    "日本語",
    "日本語 名詞",
    "日本語 形容動詞"
  ],
  "forms": [
    {
      "form": "いちじどくりつ"
    }
  ],
  "lang": "日本語",
  "lang_code": "ja",
  "pos": "noun",
  "pos_title": "名詞",
  "senses": [
    {
      "categories": [
        "日本語 線型代数学"
      ],
      "glosses": [
        "ベクトルの一次結合において、全てのスカラーが零であるときのみ、その一次結合がゼロベクトルとなること。a₁v₁ + a₂v₂ + ... + aₖvₖ = 0 であれば、a₁ = a₂ = ... = aₖ = 0 であること。"
      ],
      "topics": [
        "linear algebra"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "線形独立"
    },
    {
      "word": "線型独立"
    }
  ],
  "translations": [
    {
      "lang": "英語",
      "lang_code": "en",
      "word": "linear independence"
    },
    {
      "lang": "英語",
      "lang_code": "en",
      "word": "linearly independent"
    }
  ],
  "word": "一次独立"
}