"transition matrix" meaning in English

{
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    {
      "args": {
        "1": "en",
        "2": "transition",
        "3": "matrix"
      },
      "expansion": "transition + matrix",
      "name": "compound"
    }
  ],
  "etymology_text": "transition + matrix",
  "forms": [
    {
      "form": "transition matrices",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "transition matrixes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "transition matrices",
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      "expansion": "transition matrix (plural transition matrices or transition matrixes)",
      "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"
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "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",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "square matrix",
          "square matrix"
        ],
        [
          "nonnegative",
          "nonnegative"
        ],
        [
          "real numbers",
          "real numbers"
        ],
        [
          "Markov chain",
          "Markov chain"
        ],
        [
          "probability",
          "probability"
        ]
      ],
      "qualifier": "stochastic processes",
      "raw_glosses": [
        "(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",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "a square matrix",
          "tags": [
            "feminine"
          ],
          "word": "Übergangsmatrix"
        },
        {
          "code": "he",
          "lang": "Hebrew",
          "roman": "matrítzat ma'avarím",
          "sense": "a square matrix",
          "tags": [
            "feminine"
          ],
          "word": "מטריצת מעברים"
        }
      ],
      "wikipedia": [
        "Stochastic matrix"
      ]
    }
  ],
  "word": "transition matrix"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "transition",
        "3": "matrix"
      },
      "expansion": "transition + matrix",
      "name": "compound"
    }
  ],
  "etymology_text": "transition + matrix",
  "forms": [
    {
      "form": "transition matrices",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "transition matrixes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "transition matrices",
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      "expansion": "transition matrix (plural transition matrices or transition matrixes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "left stochastic matrix"
    }
  ],
  "senses": [
    {
      "categories": [
        "English compound terms",
        "English countable nouns",
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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."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "square matrix",
          "square matrix"
        ],
        [
          "nonnegative",
          "nonnegative"
        ],
        [
          "real numbers",
          "real numbers"
        ],
        [
          "Markov chain",
          "Markov chain"
        ],
        [
          "probability",
          "probability"
        ]
      ],
      "qualifier": "stochastic processes",
      "raw_glosses": [
        "(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."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Stochastic matrix"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "stochastic matrix"
    },
    {
      "word": "probability matrix"
    },
    {
      "word": "right stochastic matrix"
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "a square matrix",
      "tags": [
        "feminine"
      ],
      "word": "Übergangsmatrix"
    },
    {
      "code": "he",
      "lang": "Hebrew",
      "roman": "matrítzat ma'avarím",
      "sense": "a square matrix",
      "tags": [
        "feminine"
      ],
      "word": "מטריצת מעברים"
    }
  ],
  "word": "transition matrix"
}