Abstract
We investigate the non-diagonal normal forms of a quadratic form on $${\mathbb{R}}^{n}$$ , in particular for n = 3. For this case it is shown that the set of normal forms is the closure of a 5-dimensional submanifold in the 6-dimensional Grassmannian of 2-dimensional subspaces of $${\mathbb{R}}^{5}$$ .
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