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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Received: 27 June 2008
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Krötz, B., Schlichtkrull, H. Normal forms for real quadratic forms. Arch. Math. 92, 129–136 (2009). https://doi.org/10.1007/s00013-008-2925-0
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DOI: https://doi.org/10.1007/s00013-008-2925-0