"row echelon form" meaning in English

{
  "forms": [
    {
      "form": "row echelon forms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "row echelon form (countable and uncountable, plural row echelon forms)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Linear algebra",
          "orig": "en:Linear algebra",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "reduced row echelon form"
        }
      ],
      "glosses": [
        "The stepped appearance of a matrix that has undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it."
      ],
      "id": "en-row_echelon_form-en-noun-WoejVC-v",
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "stepped",
          "stepped"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "pivot",
          "pivot#Noun"
        ],
        [
          "nonzero",
          "nonzero"
        ],
        [
          "number",
          "number#Noun"
        ],
        [
          "row",
          "row#Noun"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) The stepped appearance of a matrix that has undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "row echelon form",
          "word": "porrasmuoto"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "row echelon form",
          "tags": [
            "feminine"
          ],
          "word": "forma escalonada por filas"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "row echelon form",
          "word": "trappstegsform"
        }
      ],
      "wikipedia": [
        "en:row echelon form"
      ]
    }
  ],
  "word": "row echelon form"
}

{
  "derived": [
    {
      "word": "reduced row echelon form"
    }
  ],
  "forms": [
    {
      "form": "row echelon forms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "row echelon form (countable and uncountable, plural row echelon forms)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English uncountable nouns",
        "en:Linear algebra"
      ],
      "glosses": [
        "The stepped appearance of a matrix that has undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it."
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "stepped",
          "stepped"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "pivot",
          "pivot#Noun"
        ],
        [
          "nonzero",
          "nonzero"
        ],
        [
          "number",
          "number#Noun"
        ],
        [
          "row",
          "row#Noun"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) The stepped appearance of a matrix that has undergone Gaussian elimination with the result that the leading coefficient or pivot (that is, the first nonzero number from the left) of a nonzero row is to the right of the pivot of the row above it."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "en:row echelon form"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "row echelon form",
      "word": "porrasmuoto"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "row echelon form",
      "tags": [
        "feminine"
      ],
      "word": "forma escalonada por filas"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "row echelon form",
      "word": "trappstegsform"
    }
  ],
  "word": "row echelon form"
}