"transition matrix" meaning in English

See transition matrix in All languages combined, or Wiktionary

Noun

Forms: transition matrices [plural], transition matrixes [plural]
Etymology: From transition + matrix. Etymology templates: {{compound|en|transition|matrix}} transition + matrix Head templates: {{en-noun|transition matrices|+}} transition matrix (plural transition matrices or transition matrixes)
  1. (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. Wikipedia link: Stochastic matrix Categories (topical): Mathematics Synonyms: stochastic matrix, probability matrix, right stochastic matrix Related terms: left stochastic matrix Translations (a square matrix): Übergangsmatrix [feminine] (German), מטריצת מעברים (matrítzat ma'avarím) [feminine] (Hebrew)

Inflected forms

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "transition",
        "3": "matrix"
      },
      "expansion": "transition + matrix",
      "name": "compound"
    }
  ],
  "etymology_text": "From transition + matrix.",
  "forms": [
    {
      "form": "transition matrices",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "transition matrixes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "transition matrices",
        "2": "+"
      },
      "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"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Hebrew translations",
          "parents": [],
          "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": "From transition + matrix.",
  "forms": [
    {
      "form": "transition matrices",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "transition matrixes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "transition matrices",
        "2": "+"
      },
      "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",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with German translations",
        "Terms with Hebrew translations",
        "en:Mathematics"
      ],
      "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"
}

Download raw JSONL data for transition matrix meaning in English (2.2kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.