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Question: error in JordanForm

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.
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