"transformation matrix" meaning in All languages combined

{
  "forms": [
    {
      "form": "transformation matrices",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "transformation matrixes",
      "tags": [
        "plural"
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      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
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      ],
      "derived": [
        {
          "english": "electronic engineering",
          "word": "wave transformation matrix"
        }
      ],
      "examples": [
        {
          "text": "Given a linear transformation T(x) in functional form, its transformation matrix can be constructed by applying T to each vector of the standard basis, then inserting the results into the columns of the new matrix.",
          "type": "example"
        },
        {
          "text": "A transformation matrix of dimension n×m operates on a column vector of dimension m×1 to produce a row vector of dimension 1×n.",
          "type": "example"
        },
        {
          "text": "1963 [McGraw-Hill], Lawrence P. Huelsman, Circuits, Matrices and Linear Vector Spaces, 2011, Dover, page 191,\nWe would like to make as many as possible of the elements of the transformation matrix equal zero."
        },
        {
          "text": "1968 [McGraw-Hill], Granino A. Korn, Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, 2000, Dover, page 414,\nRefer to Sec. 14.8-6 for a procedure yielding transformation matrices T with the desired properties."
        },
        {
          "ref": "2005, Gerard Kim, Designing Virtual Reality Systems: The Structured Approach, Volume 1, Springer, page 47",
          "text": "The 4x4 transformation matrices are conveniently used to convert various entities expressed in different coordinate systems into another.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
      "id": "en-transformation_matrix-en-noun-epb-lS~n",
      "links": [
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          "linear algebra",
          "linear algebra"
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          "matrix",
          "matrix"
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          "linear transformation",
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        ]
      ],
      "raw_glosses": [
        "(linear algebra) A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "matrix that represents a linear transformation",
          "word": "kuvausmatriisi"
        }
      ],
      "wikipedia": [
        "transformation matrix"
      ]
    }
  ],
  "word": "transformation matrix"
}

{
  "derived": [
    {
      "english": "electronic engineering",
      "word": "wave transformation matrix"
    }
  ],
  "forms": [
    {
      "form": "transformation matrices",
      "tags": [
        "plural"
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    },
    {
      "form": "transformation matrixes",
      "tags": [
        "plural"
      ]
    }
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  "lang_code": "en",
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        "Terms with Finnish translations",
        "en:Linear algebra"
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      "examples": [
        {
          "text": "Given a linear transformation T(x) in functional form, its transformation matrix can be constructed by applying T to each vector of the standard basis, then inserting the results into the columns of the new matrix.",
          "type": "example"
        },
        {
          "text": "A transformation matrix of dimension n×m operates on a column vector of dimension m×1 to produce a row vector of dimension 1×n.",
          "type": "example"
        },
        {
          "text": "1963 [McGraw-Hill], Lawrence P. Huelsman, Circuits, Matrices and Linear Vector Spaces, 2011, Dover, page 191,\nWe would like to make as many as possible of the elements of the transformation matrix equal zero."
        },
        {
          "text": "1968 [McGraw-Hill], Granino A. Korn, Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, 2000, Dover, page 414,\nRefer to Sec. 14.8-6 for a procedure yielding transformation matrices T with the desired properties."
        },
        {
          "ref": "2005, Gerard Kim, Designing Virtual Reality Systems: The Structured Approach, Volume 1, Springer, page 47",
          "text": "The 4x4 transformation matrices are conveniently used to convert various entities expressed in different coordinate systems into another.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
      "links": [
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "matrix",
          "matrix"
        ],
        [
          "linear transformation",
          "linear transformation"
        ]
      ],
      "raw_glosses": [
        "(linear algebra) A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
      "topics": [
        "linear-algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
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      ]
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  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "matrix that represents a linear transformation",
      "word": "kuvausmatriisi"
    }
  ],
  "word": "transformation matrix"
}