Part of a vector space spanned by a given spanning set.

The subspace of a vector space \(\mathcal{V}\) is a subset of \(\mathcal{V}\) is also a vector space.

E.g. span of a set of vectors of \(\mathcal{V}\).


If \(S\) is a nonempty subset of a vector space \(V\), and \(S\) satisfies the conditions:

  1. \(\alpha |x\rangle\in S\) whenever \(|x\rangle\in S\) for any scalar \(\alpha\)
  2. \(|x\rangle + |y\rangle\in S\) whenever \(|x\rangle\in S\) and \(|y\rangle\in S\)

then \(S\) is said to be a subspace of \(V\).

Author: Christian Cunningham

Created: 2023-06-25 Sun 02:26