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"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": "60 40", "word": "characteristic equation" }, { "_dis1": "60 40", "word": "characteristic root" }, { "_dis1": "60 40", "word": "characteristic vector" }, { "_dis1": "60 40", "word": "minimal polynomial" }, { "_dis1": "60 40", "word": "eigenvector" }, { "_dis1": "60 40", "word": "eigenvalue" } ], "topics": [ "linear-algebra", "mathematics", "sciences" ], "translations": [ { "_dis1": "60 40", "code": "et", "lang": "Estonian", "sense": "linear algebra", "word": "karakteristlik polünoom" }, { "_dis1": "60 40", "code": "fi", "lang": "Finnish", "sense": "linear algebra", "word": "karakteristinen polynomi" }, { "_dis1": "60 40", "code": "fr", "lang": "French", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polynôme caractéristique" }, { "_dis1": "60 40", "code": "de", "lang": "German", "sense": "linear algebra", "tags": [ "neuter" ], "word": "charakteristiches Polynom" }, { "_dis1": "60 40", "code": "hu", "lang": "Hungarian", "sense": "linear algebra", "word": "karakterisztikus polinom" }, { "_dis1": "60 40", "code": "it", "lang": "Italian", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polinomio caratteristico" }, { "_dis1": "60 40", "code": "pt", "lang": "Portuguese", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polinómio característico" }, { "_dis1": "60 40", "code": "pt", "lang": "Portuguese", "sense": "linear algebra", "tags": [ "Brazil", "masculine" ], "word": "polinômio característico" }, { "_dis1": "60 40", "code": "ro", "lang": "Romanian", "sense": "linear algebra", "tags": [ "neuter" ], "word": "polinom caracteristic" }, { "_dis1": "60 40", "code": "es", "lang": "Spanish", "sense": "linear algebra", "tags": [ "masculine" ], "word": "polinomio característico" }, { "_dis1": "60 40", "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": "55 45", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "41 59", "kind": "other", "name": "English entries with topic categories using raw markup", "parents": [ "Entries with topic categories using raw markup", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "51 49", "kind": "other", "name": "English terms with non-redundant non-automated sortkeys", "parents": [ "Terms with non-redundant non-automated sortkeys", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "51 49", "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w+disamb" }, { "_dis": "50 50", "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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