= Radical of a Hermitian form
{title2=$\operatorname{rad}h=\{v:h(v,w)=0\text{ for all }w\}$}
The radical of a <Hermitian form> is the <vector subspace> orthogonal to the entire space. The form descends to the <quotient vector space> by its radical: adding a radical <vector> to either argument does not change the value. For a <positive semidefinite Hermitian form>, the <Cauchy-Schwarz inequality> identifies this radical with its zero-norm <vectors>, so the quotient form is positive definite. This conclusion does not hold for a general <indefinite Hermitian form>: a zero-norm <vector> need not belong to its radical.
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