= Indefinite Hermitian form
{title2=$\langle v,v\rangle\ \text{can have either sign}$}
= Indefinite inner product
{synonym}
An indefinite <Hermitian form> takes both positive and negative values on $\langle v,v\rangle$ for nonzero <vectors>. For example, $-|v_0|^2+|v_1|^2+|v_2|^2+|v_3|^2$ is indefinite. It is not a positive <inner product> defining a <Hilbert space>, and a nonzero <vector> can have zero norm without being orthogonal to all <vectors>. A positive semidefinite restricted form becomes a positive <inner product> only after quotienting its <radical of a Hermitian form>.
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