How to find the permutation matrix associated with the similarity transformation in the following code

asked 2017-11-13 12:23:18 -0600

anonymous user

Anonymous

m = matrix(QQbar,6,[2,-1,-I,0,0,0, -1,2,-1,0,0,0,i,-1,3,-1,0,0, 0,0,-1,2,-1,0, 0,0,0,-1,2,-1, 0,0,0,0,-1,1])

j=matrix(QQbar,6,[2,-1,0,-I,0,0, -1,2,-1,0,0,0,0,-1,2,-1,0,0, I,0,-1,3,0,-1, 0,0,0,0,1,-1, 0,0,0,-1,-1,2])

the matrices m,j are similar via a permutation matrix. How I can find that matrix.

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Comments

Have you read the answers to this question, in particular Dan's?

B r u n o gravatar imageB r u n o ( 2017-11-13 12:51:29 -0600 )edit

The following code searches for permutation matrices $S$ that satisfy $MS=SJ$.

F.<v> = QuadraticField( -1 )
M = matrix( F, 6,
            [  2,-1,-v, 0, 0, 0,
              -1, 2,-1, 0, 0, 0,
               v,-1, 3,-1, 0, 0,
               0, 0,-1, 2,-1, 0,
               0, 0, 0,-1, 2,-1,
               0, 0, 0, 0,-1, 1, ] )

J = matrix( F, 6,
            [   2,-1, 0,-v, 0, 0,
               -1, 2,-1, 0, 0, 0,
                0,-1, 2,-1, 0, 0,
                v, 0,-1, 3, 0,-1,
                0, 0, 0, 0, 1,-1,
                0, 0, 0,-1,-1, 2, ] )

for s in SymmetricGroup(6):
    S = s.matrix()
    if M*S == S*J:
        print S

Nothing found.

Which is the source of the problem?

dan_fulea gravatar imagedan_fulea ( 2017-11-13 17:54:36 -0600 )edit

m = matrix(QQbar,6,[2,-1,-I,0,0,0, -1,2,-1,0,0,0,i,-1,3,-1,0,0, 0,0,-1,2,-1,0, 0,0,0,-1,2,-1, 0,0,0,0,-1,1]) n = matrix(QQbar,6,[2,-1,0,-I,0,0,-1,2,-1,0,0,0,0,-1,2,-1,0,0,i,0,-1,3,-1,0,0,0,0,-1,2,-1, 0,0,0,0,-1,1]) Actually the problem was as follows: Suppose we find out the all possible permutation similar matrices for both the matrices m,n. Now I want to take the intersection of these two set of collections

A gravatar imageA ( 2017-11-14 01:47:43 -0600 )edit