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Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.

9 votes
1 answer
2k views

Over which fields is the Sylvester law of inertia valid?

Short version: Over which fields is the (appropriate version of the) "Sylvester law of inertia" valid? Long version: Let $V$ be a finite dimensional vector space over the field $\Bbbk$ of char …
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0 votes
0 answers
173 views

Topological vs algebraic intersection forms

Let $X$ be a simply connected complex projective surface (hence a real $4$-manifold). Let $(H^2(X,\mathbb Z)/\mathrm{tors}, q_X)$, $(A^1(X)/\mathrm{tors},q_X')$ be the corresponding lattices in cohomo …
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21 votes
1 answer
12k views

Non-diagonalizable complex symmetric matrix

This is a question in elementary linear algebra, though I hope it's not so trivial to be closed. Real symmetric matrices, complex hermitian matrices, unitary matrices, and complex matrices with disti …
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