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A linear algebra question for semi-Euclidean norm

Let us consider Minkowski inner product on $\mathbb R^{1+n}$, defined by $$ \langle v,w \rangle = -v_0w_0+\sum_{j=1}^n v_j w_j\quad \,\forall\, v,w \in \mathbb R^{1+n}.$$ We say that a vector $v$ is ...
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Complex conjugate and unitary complex conjugate

Definition: Let V be complex finite dimensional inner product space Complex Conjugate: $J$ is called complex conjugate on V iff $(i) J$ is antilinear $(ii) J^2 =I$ Definition: Anti-unitary Complex ...