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Bug in eigenmatrix command?

I'm new to sage, so this might be my bad, but I think there is a mismatch between complex conjugate eigevector/values in what the eigenmatrix_right() returns:

In my case:

J = matrix(CDF, [[-2.53634347567,  2.04801738686, -0.0, -62.166145304], [ 0.7, -0.6, 0.0, 0.0], [0.547271128842, 0.0, -0.3015, -21.7532081652], [0.0, 0.0, 0.3, -0.4]])
D, P = J.eigenmatrix_right()

D has two (almost) purely imaginary complex conjugate eigenvalues. I thought

A1 = J * P

and

A2 =  P * D

should be identical, but the complex conjugate eigenvalues are interchanged, so two columns in A1 and A2 differ by a multiple of (-1). In my case things work ok if I interchange D[1][1] and D[2][2].

Am I missing something?

Bug in eigenmatrix command?

I'm new to sage, so this might be my bad, but I think there is a mismatch between complex conjugate eigevector/values in what the eigenmatrix_right() returns:

In my case:

J = matrix(CDF, [[-2.53634347567,  2.04801738686, -0.0, -62.166145304], [ 0.7, -0.6, 0.0, 0.0], [0.547271128842, 0.0, -0.3015, -21.7532081652], [0.0, 0.0, 0.3, -0.4]])
D, P = J.eigenmatrix_right()

D has two (almost) purely imaginary complex conjugate eigenvalues. I thought

A1 = J * P

and

A2 =  P * D

should be identical, but the complex conjugate eigenvalues are interchanged, so two columns in A1 and A2 differ by a multiple of (-1). In my case things work ok if I interchange D[1][1] and D[2][2].

Am I missing something?