On 2/27/12 6:30 AM, John Cremona wrote:
In 4.8, I have a 3x3 matrix T over a quadratic number field but when I
ask for T.eigenvalues() I get a list of 6 elements of QQbar, and
T.eigenmatrix_right() returns a pair of 6x6 matrices.
Please tell me that this is a bug and not a feature!
John
sage: TK.parent()
Full MatrixSpace of 3 by 3 dense matrices over Number Field in a with
defining polynomial x^2 + 7
sage: TK
[ 1 -a 2]
[ -1 1/2*a - 1/2 -1]
[ -1 1/2*a - 3/2 -1]
sage: len(TK.eigenvalues())
6
sage: TK.eigenmatrix_left()[0].parent()
Full MatrixSpace of 6 by 6 sparse matrices over Algebraic Field
Further, look at the dimension of the eigenvector matrix:
sage: R=QuadraticField(-7,'a')
sage: a=R.0
sage: TK=matrix(3,[1,-a,2,-1,a/2-1/2,-1,-1,a/2-3/2,-1])
sage: D,P=TK.eigenmatrix_left()
sage: D.parent()
Full MatrixSpace of 6 by 6 sparse matrices over Algebraic Field
sage: P.parent()
Full MatrixSpace of 6 by 3 dense matrices over Algebraic Field
Jason
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