"transition matrix" meaning in English

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      "expansion": "transition + matrix",
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  "etymology_text": "From transition + matrix.",
  "forms": [
    {
      "form": "transition matrices",
      "tags": [
        "plural"
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      "form": "transition matrixes",
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        "plural"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the ith row and jth column describes the probability of moving from state i to state j in one time step."
      ],
      "id": "en-transition_matrix-en-noun-SzvR9c0X",
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          "mathematics",
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          "square matrix",
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          "nonnegative"
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        [
          "real numbers",
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          "Markov chain",
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        [
          "probability",
          "probability"
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      "qualifier": "stochastic processes",
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        "(mathematics, stochastic processes) A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the ith row and jth column describes the probability of moving from state i to state j in one time step."
      ],
      "related": [
        {
          "word": "left stochastic matrix"
        }
      ],
      "synonyms": [
        {
          "word": "stochastic matrix"
        },
        {
          "word": "probability matrix"
        },
        {
          "word": "right stochastic matrix"
        }
      ],
      "topics": [
        "mathematics",
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      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "a square matrix",
          "tags": [
            "feminine"
          ],
          "word": "Übergangsmatrix"
        },
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          "code": "he",
          "lang": "Hebrew",
          "roman": "matrítzat ma'avarím",
          "sense": "a square matrix",
          "tags": [
            "feminine"
          ],
          "word": "מטריצת מעברים"
        }
      ],
      "wikipedia": [
        "Stochastic matrix"
      ]
    }
  ],
  "word": "transition matrix"
}

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  ],
  "etymology_text": "From transition + matrix.",
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    {
      "form": "transition matrices",
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  "lang_code": "en",
  "pos": "noun",
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      "word": "left stochastic matrix"
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        "A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the ith row and jth column describes the probability of moving from state i to state j in one time step."
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        "(mathematics, stochastic processes) A square matrix whose rows consist of nonnegative real numbers, with each row summing to 1. Used to describe the transitions of a Markov chain; its element in the ith row and jth column describes the probability of moving from state i to state j in one time step."
      ],
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        "mathematics",
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      "word": "probability matrix"
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  "translations": [
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      "code": "de",
      "lang": "German",
      "sense": "a square matrix",
      "tags": [
        "feminine"
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      "word": "Übergangsmatrix"
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      "lang": "Hebrew",
      "roman": "matrítzat ma'avarím",
      "sense": "a square matrix",
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  "word": "transition matrix"
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