Then, the same concept follows : any operator is the sum of a Hermitian operator and an anti-Hermitian one, so if time is some kind of disturbance in a Hermitian space, the CPT-symmetric laws will amplify, and the CPT-antisymmetric laws will cancel.
2.
Often for reasons of geometric interest this is specialized to a subcategory, by requiring that the nondegenerate bilinear forms have additional properties, such as being symmetric ( orthogonal matrices ), symmetric and positive definite ( inner product space ), symmetric sesquilinear ( Hermitian spaces ), skew-symmetric and totally isotropic ( symplectic vector space ), etc . in all these categories a vector space is naturally identified with its dual, by the nondegenerate bilinear form.
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