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Issimilar

determine similarity of matrices

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Issimilar(A, B)

Issimilar(A, B, 'P')

Parameters

A

-

square Matrix

B

-

square Matrix

'P'

-

(optional) assigned a transformation matrix

Description

• 

The function Issimilar(A, B) is a placeholder for the boolean valued function that returns true if A is similar to B and false otherwise.  It is used in conjunction with either mod or evala.

• 

If called in the form Issimilar(A, B,'P'), then P will be assigned a transformation matrix such that A=inversePBP.

• 

The call Issimilar(A, B) mod p determines if A is similar to B modulo p which is a prime integer.  The entries of A and B must have rational coefficients or coefficients from an algebraic extension of the integers modular p.

• 

The call evala(Issimilar(A, B)) determines if A is similar to B where the entries of A and B are algebraic numbers (or functions) defined by RootOfs.

Examples

withLinearAlgebra:

AMatrix1,2,3,4,5,6,7,8,9

A:=123456789

(1)

p11

p:=11

(2)

cACharacteristicPolynomialA,xmodp

cA:=x3+7x2+4x

(3)

BCompanionMatrixcA,x

B:=000104017

(4)

IssimilarA,B,'P'modp

true

(5)

P

868823100

(6)

P1.B.Pmod11

123456789

(7)

See Also

Domains

LinearAlgebra

LinearAlgebra[IsSimilar]

LinearAlgebra[Modular]

mod

 


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