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The polynomial produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant.
Definition source: English Wiktionary via Wiktextract
Topics: linear-algebra, mathematics, sciences
Examples
- The characteristic polynomial of #92;textstyle#92;left(#92;begin#123;array#125;#123;cc#125;1amp;4#92;#92;3amp;-5#92;end#123;array#125;#92;right) is #92;textstyle#92;left#92;vert#92;begin#123;array#125;#123;cc#125;1-xamp;4#92;#92;3amp;-5-x#92;end#123;array#125;#92;right#92;vert#61;x2#43;4x-17.
- The characteristic polynomial of a 2#92;times 2 matrix M is #92;lambda2-#92;mbox#123;tr#125;(M)#92;lambda#43;#92;mbox#123;det#125;(M), where #92;mbox#123;tr#125;(M) denotes the trace of M and #92;mbox#123;det#125;(M) denotes the determinant of M.
- The characteristic polynomial of a 3#92;times 3 matrix M is -#92;lambda3#43;#92;mbox#123;tr#125;(M)#92;lambda2-#92;mbox#123;tr#125;(#92;mbox#123;adj#125;(M))#92;lambda#43;#92;mbox#123;det#125;(M), where #92;mbox#123;adj#125;(M) denotes the adjugate of M.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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).
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
14 source translations are retained for this English entry.
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Asturian:
polinomiu característicu
— linear algebra
-
Chinese Mandarin:
特徵多項式 /特征多项式
— linear algebra
-
Estonian:
karakteristlik polünoom
— linear algebra
-
Finnish:
karakteristinen polynomi
— linear algebra
-
French:
polynôme caractéristique
— linear algebra
-
German:
charakteristiches Polynom
— linear algebra
-
Hungarian:
karakterisztikus polinom
— linear algebra
-
Italian:
polinomio caratteristico
— linear algebra
-
Polish:
wielomian charakterystyczny
— linear algebra
-
Portuguese:
polinómio característico
— linear algebra
-
Portuguese:
polinômio característico
— linear algebra
-
Romanian:
polinom caracteristic
— linear algebra
-
Spanish:
polinomio característico
— linear algebra
-
Swedish:
karakteristiskt polynom
— linear algebra
