# Invariants and syzygies for 3x3 matrices

I'm interested in the structure of the scalars formed from a real 3x3 matrix which are invariant under conjugation by orthogonal matrices, i.e. bases, syzygies, and other stuff. Does anyone know a good reference?

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Perhaps i should make my question a bit more precise. What I'm interested in are the polynomial invariants of a real 3x3 matrix, more precisely in the scalars that can be expressed as polynomials in the matrix entries and that are invariant under a rotation of the coordinate system. I would like to construct bases and to analyze relations among the (basis) invariants, like syzygies. –  Daniel Lengeler Feb 28 at 12:12