In this paper, we give some conditions to judge when a system of Hermitian quadratic forms has a real linear combination which is positive definite or positive semi-definite. We also study some related geometric and topological properties of the moduli space.

Keywords:

hermitian quadratic form, positive definite, positive semi-definite hermitian quadratic form, positive definite, positive semi-definite

MSC Classifications:

15A63 show english descriptions Quadratic and bilinear forms, inner products [See mainly 11Exx] 15A63 - Quadratic and bilinear forms, inner products [See mainly 11Exx]

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