Quadratic form

Q=ab+bc+da+cd
How to diagonalized it?
I thing I should write it as a Matrix first and then just diagonalized that matrix but I'm not sure how should that matrix look like.
main seggestion.

1/2 0 1/2 0
1/2 1/2 0 0
1/2 0 1/2 0
1/2 0 0 1/2

Thanks for any suggestions from you sites.
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