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Student[LinearAlgebra]

  

MinimalPolynomial

  

construct the minimal polynomial of a Matrix

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MinimalPolynomial(A, t)

Parameters

A

-

Matrix

t

-

name; variable

Description

• 

The MinimalPolynomial(A, t) command returns a polynomial in t that is the minimal polynomial of Matrix A.

  

The minimal polynomial of A is the polynomial of lowest degree that divides every polynomial which has A as a zero.

Examples

withStudent[LinearAlgebra]:

A3,0,1|1,2,1|0,0,2

A:=310020112

(1)

mpMinimalPolynomialA,x

mp:=x25x+6

(2)

divideCharacteristicPolynomialA,x,mp

true

(3)

Punapplymp,x

P:=x→x25x+6

(4)

PA

000000000

(5)

See Also

divide

LinearAlgebra[MinimalPolynomial]

Student[LinearAlgebra]

Student[LinearAlgebra][CharacteristicMatrix]

Student[LinearAlgebra][CharacteristicPolynomial]

unapply

 


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