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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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Existence of solutions to quadratic vector equation
Given
$$A_{i,j,k} X_j^* X_k + C_i = 0$$
where $𝐴_{i,j,k}$ and $𝐶_i$ are arbitrary complex numbers for all $𝑗, 𝑘$ which are $𝑁$-dimensional indices and $i$ which is an $m$-dimensional index where …