Closed linear span
= Closed linear span
{title2=$\overline{\operatorname{span}}S$}
In a <normed vector space>, the closed linear span of $S$ is the <closure> of its <linear span> in the <norm topology>. It includes <limits> of finite <linear combinations>. In a <Hilbert space>, an infinite <orthonormal basis> spans in this closed sense, allowing norm-convergent series in addition to finite sums.