"transformation matrix" meaning in All languages combined

{
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    {
      "form": "transformation matrices",
      "tags": [
        "plural"
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    {
      "form": "transformation matrixes",
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        "plural"
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  "lang": "English",
  "lang_code": "en",
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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": "quote"
        }
      ],
      "glosses": [
        "A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
      "id": "en-transformation_matrix-en-noun-epb-lS~n",
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      "raw_glosses": [
        "(linear algebra) A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
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        "linear-algebra",
        "mathematics",
        "sciences"
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      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "matrix that represents a linear transformation",
          "word": "kuvausmatriisi"
        }
      ],
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  "word": "transformation matrix"
}

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      "english": "electronic engineering",
      "word": "wave transformation matrix"
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      "form": "transformation matrices",
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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": "quote"
        }
      ],
      "glosses": [
        "A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
      "links": [
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        "(linear algebra) A matrix (of dimension n×m) that represents some linear transformation from ℝᵐ→ℝⁿ."
      ],
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        "linear-algebra",
        "mathematics",
        "sciences"
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  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "matrix that represents a linear transformation",
      "word": "kuvausmatriisi"
    }
  ],
  "word": "transformation matrix"
}