See invertible matrix on Wiktionary
{
"antonyms": [
{
"word": "singular matrix"
},
{
"word": "degenerate matrix"
}
],
"forms": [
{
"form": "invertible matrices",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "invertible matrices"
},
"expansion": "invertible matrix (plural invertible matrices)",
"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 Finnish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Japanese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Polish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Romanian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Swedish translations",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Linear algebra",
"orig": "en:Linear algebra",
"parents": [
"Algebra",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"text": "1975 [Prentice-Hall], Kenneth Hoffman, Analysis in Euclidean Space, Dover, 2007, page 65,\nIt says that, if A is a singular matrix, then every neighborhood of A contains an invertible matrix. In other words, if A is singular, we can perturb A just a little and obtain an invertible matrix."
},
{
"ref": "1997, Bernard L. Johnston, Fred Richman, Numbers and Symmetry: An Introduction to Algebra, CRC Press, page 199:",
"text": "There are certain very simple invertible matrices, and every invertible matrix over a field can be built up out of them.",
"type": "quote"
},
{
"ref": "2013, Mahya Ghandehari, Aizhan Syzdykova, Keith F. Taylor, “A four dimensional continuous wavelet transform”, in Azita Mayeli, editor, Commutative and Noncommutative Harmonic Analysis and Applications, American Mathematical Society, page 123:",
"text": "The space of real square matrices of fixed size is a vector space whose dimension is a perfect square and the invertible matrices constitute a dense open subset of this vector space.",
"type": "quote"
}
],
"glosses": [
"Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
],
"hyponyms": [
{
"word": "unitary matrix"
}
],
"id": "en-invertible_matrix-en-noun-X~ibcDka",
"links": [
[
"linear algebra",
"linear algebra"
],
[
"square",
"square"
],
[
"inverse matrix",
"inverse matrix"
],
[
"identity matrix",
"identity matrix"
]
],
"raw_glosses": [
"(linear algebra) Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
],
"topics": [
"linear-algebra",
"mathematics",
"sciences"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "kääntyvä matriisi"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "invertierbare Matrix"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "reguläre Matrix"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "invertálható mátrix"
},
{
"code": "it",
"lang": "Italian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "matrice invertibile"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "seisoku gyōretsu",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "正則行列"
},
{
"code": "pl",
"lang": "Polish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "macierz odwrotna"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "matrice inversabilă"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"common-gender"
],
"word": "inverterbar matris"
}
],
"wikipedia": [
"invertible matrix"
]
}
],
"word": "invertible matrix"
}
{
"antonyms": [
{
"word": "singular matrix"
},
{
"word": "degenerate matrix"
}
],
"forms": [
{
"form": "invertible matrices",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "invertible matrices"
},
"expansion": "invertible matrix (plural invertible matrices)",
"name": "en-noun"
}
],
"hyponyms": [
{
"word": "unitary matrix"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Finnish translations",
"Terms with German translations",
"Terms with Hungarian translations",
"Terms with Italian translations",
"Terms with Japanese translations",
"Terms with Polish translations",
"Terms with Romanian translations",
"Terms with Swedish translations",
"en:Linear algebra"
],
"examples": [
{
"text": "1975 [Prentice-Hall], Kenneth Hoffman, Analysis in Euclidean Space, Dover, 2007, page 65,\nIt says that, if A is a singular matrix, then every neighborhood of A contains an invertible matrix. In other words, if A is singular, we can perturb A just a little and obtain an invertible matrix."
},
{
"ref": "1997, Bernard L. Johnston, Fred Richman, Numbers and Symmetry: An Introduction to Algebra, CRC Press, page 199:",
"text": "There are certain very simple invertible matrices, and every invertible matrix over a field can be built up out of them.",
"type": "quote"
},
{
"ref": "2013, Mahya Ghandehari, Aizhan Syzdykova, Keith F. Taylor, “A four dimensional continuous wavelet transform”, in Azita Mayeli, editor, Commutative and Noncommutative Harmonic Analysis and Applications, American Mathematical Society, page 123:",
"text": "The space of real square matrices of fixed size is a vector space whose dimension is a perfect square and the invertible matrices constitute a dense open subset of this vector space.",
"type": "quote"
}
],
"glosses": [
"Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
],
"links": [
[
"linear algebra",
"linear algebra"
],
[
"square",
"square"
],
[
"inverse matrix",
"inverse matrix"
],
[
"identity matrix",
"identity matrix"
]
],
"raw_glosses": [
"(linear algebra) Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix)."
],
"topics": [
"linear-algebra",
"mathematics",
"sciences"
],
"wikipedia": [
"invertible matrix"
]
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "kääntyvä matriisi"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "invertierbare Matrix"
},
{
"code": "de",
"lang": "German",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "reguläre Matrix"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "invertálható mátrix"
},
{
"code": "it",
"lang": "Italian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "matrice invertibile"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "seisoku gyōretsu",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"word": "正則行列"
},
{
"code": "pl",
"lang": "Polish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "macierz odwrotna"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"feminine"
],
"word": "matrice inversabilă"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "square matrix which, when multiplied by some other, yields the identity matrix",
"tags": [
"common-gender"
],
"word": "inverterbar matris"
}
],
"word": "invertible matrix"
}
Download raw JSONL data for invertible matrix meaning in All languages combined (4.3kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.