Consider the following symmetric matrix
A:=Matrix([[1,sqrt(2),-sqrt(6)],[sqrt(2),2,sqrt(3)],[-sqrt(6),sqrt(3),0]]);
If I compute the Jordan canonical form using JordanForm from the LinearAlgebra package, I get
[-3 0 0]
[ ]
[ 0 3 1]
[ ]
[ 0 0 3]
This is obviously false, since every symmetric matrix is diagonalizable.
