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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.
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When the summands of a positive definite matrix are positive definite
Let $A,B$ be two real symmetric matrices. Let $C = A+B$ be a positive-definite matrix. Write $C>0$ for $C$ being positive-definite. Suppose that $A>0 \implies C>0$ and $B > 0 \implies C>0$, can anythi …