On spinors

For a 2 ⁿ -dimensional complex Hermitian vector space S, we prove that any unitary basis of S can be explained as an augmented spinor structure on S. By using this explanation, a Spin ^c (2n)-action on S is equivalent to an action on a subset of augmented spinor structures. The latter action is a little easy to be understood, and is shown in the last part of this paper. Such kind of understanding could be of use to the discussions of Hermitian manifolds and spin manifolds, especially could help to find connections and elliptical operators.