See characteristic polynomial on Wiktionary
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produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant." ], "id": "en-characteristic_polynomial-en-noun-aJsN4Lc6", "links": [ [ "linear algebra", "linear algebra" ], [ "polynomial", "polynomial" ], [ "square matrix", "square matrix" ], [ "identity matrix", "identity matrix" ], [ "indeterminant", "indeterminant" ], [ "determinant", "determinant" ] ], "raw_glosses": [ "(linear algebra) The polynomial produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant." ], "related": [ { "_dis1": "61 39", "word": "characteristic equation" }, { "_dis1": "61 39", "word": "characteristic root" }, { "_dis1": "61 39", "word": "characteristic vector" }, { "_dis1": "61 39", "word": "minimal polynomial" }, { "_dis1": "61 39", "word": "eigenvector" }, { "_dis1": "61 39", "word": "eigenvalue" } ], "topics": [ "linear-algebra", "mathematics", "sciences" ], "translations": [ { "_dis1": "56 44", "code": "et", "lang": "Estonian", "sense": "linear algebra", "word": "karakteristlik polünoom" }, { "_dis1": "56 44", "code": "fi", "lang": "Finnish", "sense": "linear algebra", "word": "karakteristinen polynomi" }, { "_dis1": "56 44", "code": "fr", "lang": "French", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polynôme caractéristique" }, { "_dis1": "56 44", "code": "de", "lang": "German", "sense": "linear algebra", "tags": [ "neuter" ], "word": "charakteristiches Polynom" }, { "_dis1": "56 44", "code": "hu", "lang": "Hungarian", "sense": "linear algebra", "word": "karakterisztikus polinom" }, { "_dis1": "56 44", "code": "it", "lang": "Italian", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polinomio caratteristico" }, { "_dis1": "56 44", "code": "pt", "lang": "Portuguese", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polinómio característico" }, { "_dis1": "56 44", "code": "pt", "lang": "Portuguese", "sense": "linear algebra", "tags": [ "Brazil", "masculine" ], "word": "polinômio característico" }, { "_dis1": "56 44", "code": "ro", "lang": "Romanian", "sense": "linear algebra", "tags": [ "neuter" ], "word": "polinom caracteristic" }, { "_dis1": "56 44", "code": "es", "lang": "Spanish", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polinomio característico" }, { "_dis1": "56 44", "code": "sv", "lang": "Swedish", "sense": "linear algebra", "tags": [ "neuter" ], "word": "karakteristiskt polynom" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "36 64", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "22 78", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "36 64", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "27 73", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "30 70", "kind": "other", "name": "Terms with Estonian translations", "parents": [], "source": "w+disamb" }, { "_dis": "28 72", "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w+disamb" }, { "_dis": "27 73", "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w+disamb" }, { "_dis": "26 74", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "37 63", "kind": "other", "name": "Terms with Hungarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "26 74", "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" }, { "_dis": "30 70", "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "24 76", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "29 71", "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w+disamb" }, { "_dis": "42 58", "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w+disamb" }, { "_dis": "41 59", "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w+disamb" } ], "glosses": [ "A polynomial P(r) corresponding to a homogeneous, linear, ordinary differential equation P(D) y = 0 where D is a differential operator (with respect to a variable t, if y is a function of t)." ], "id": "en-characteristic_polynomial-en-noun-kT7KyV0v", "links": [ [ "mathematics", "mathematics" ], [ "homogeneous", "homogeneous" ], [ "linear", "linear" ], [ "ordinary differential equation", "ordinary differential equation" ], [ "differential operator", "differential operator" ] ], "raw_glosses": [ "(mathematics) A polynomial P(r) corresponding to a homogeneous, linear, ordinary differential equation P(D) y = 0 where D is a differential operator (with respect to a variable t, if y is a function of t)." ], "topics": [ "mathematics", "sciences" ] } ], "wikipedia": [ "characteristic polynomial" ], "word": "characteristic polynomial" }
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-02-17 from the enwiktionary dump dated 2025-02-02 using wiktextract (ca09fec and c40eb85). 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.
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