= Quotient Hermitian metric
{title2=$h_Q([v],[w])=h_E((I-\pi_S)v,(I-\pi_S)w)$}
For a smooth subbundle $S$ of a <Hermitian vector bundle> $E$, <orthogonal projection> identifies $E/S$ smoothly with $S^\perp$. The quotient metric is $h_Q([v],[w])=h_E((I-\pi_S)v,(I-\pi_S)w)$. It is independent of representatives and positive definite. For a holomorphic subbundle the resulting smooth quotient metric is defined on the holomorphic quotient, but the orthogonal identification itself need not be holomorphic.
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