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Student[LinearAlgebra]

  

CharacteristicPolynomial

  

construct the characteristic polynomial of a Matrix

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

CharacteristicPolynomial(A, t)

Parameters

A

-

Matrix

t

-

name; variable

Description

• 

The CharacteristicPolynomial(A, t) command returns the characteristic polynomial in t that has the eigenvalues of Matrix A as its roots (all multiplicities respected).

  

This polynomial is the determinant of IdtA, where Id is the identity Matrix with Dimension(A).

Examples

withStudent[LinearAlgebra]:

M1,0,0|1,1,0|0,3,2

M:=110013002

(1)

CharacteristicPolynomialM,x

x34x2+5x2

(2)

solve,x

2,1,1

(3)

EigenvaluesM

211

(4)

See Also

LinearAlgebra[CharacteristicPolynomial]

solve

Student[LinearAlgebra]

Student[LinearAlgebra][CharacteristicMatrix]

Student[LinearAlgebra][Eigenvalues]

Student[LinearAlgebra][IdentityMatrix]

Student[LinearAlgebra][MinimalPolynomial]

 


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