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Characteristic polynomial

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix among its coefficients. The characteristic polynomial of an endomorphism of a finite-dimensional vector space is the characteristic polynomial…

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Examples

Properties

Characteristic polynomial of Ak

Secular function and secular equation

For general associative algebras

Theoretical complexity: calculation by fast matrix multiplication

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Characteristic polynomial

Nodes62
Edges61
Triples52
Avg. degree1.97
Density0.032258
Components1

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Characteristic polynomial

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related to References · 26
Characteristic polynomial → Addison-Wesley ISBN, American Mathematical Monthly, Basic Linear Algebra, Beauregard, Blyth, Brooks/Cole ISBN, Elementary Linear Algebra, Fraleigh, Garibaldi, Gilbert Strang, Greub, ISBN, Its Applications, John, JSTOR, Linear Algebra, MR, Paul, Raymond, Robertson
related to Characteristic polynomial of a product of two matrices · 5
Characteristic polynomial → AB, Av, BA, If, Therefore
related to Formal definition · 5
Characteristic polynomial → A-tI, Consider, Some, That, The
related to Examples · 4
Characteristic polynomial → Another, For, Its, To
related to Properties · 4
Characteristic polynomial → All, For, In, The
related to For general associative algebras · 2
Characteristic polynomial → Garibaldi, The
related to Secular function · 2
Characteristic polynomial → Lagrange's, The
related to Theoretical complexity: calculation by fast matrix multiplication · 2
Characteristic polynomial → It, Respective

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Important terminology

characteristic displaystyle polynomial matrix lambda det times linear algebra eigenvalues equation square matrices ab field determinant trace -1 tr textstyle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the complex numbers.ProofThis proof only applies to matricesinstance ofunless the matrix is over an algebraically closed field0.80text
polynomials over complex numbersinstance ofunless the matrix is over an algebraically closed field0.80text
Characteristic polynomialrelated to Characteristic polynomial of a product of two matricesIf0.60section
Characteristic polynomialrelated to Characteristic polynomial of a product of two matricesAB0.60section
Characteristic polynomialrelated to Characteristic polynomial of a product of two matricesBA0.60section
Characteristic polynomialrelated to Characteristic polynomial of a product of two matricesAv0.60section
Characteristic polynomialrelated to Characteristic polynomial of a product of two matricesTherefore0.60section
Characteristic polynomialrelated to ExamplesTo0.60section
Characteristic polynomialrelated to ExamplesAnother0.60section
Characteristic polynomialrelated to ExamplesFor0.60section
Characteristic polynomialrelated to ExamplesIts0.60section
Characteristic polynomialrelated to For general associative algebrasThe0.60section

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