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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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Proof of A Positive Definite Covariance Matrix

To elaborate a bit on Mahdi's comment, recall that a positive definite matrix $\Sigma$ can be used to define a scalar product, i.e. $\langle a,b \rangle := a^\top\Sigma\, b$, and $\langle a,a\rangle = …
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