I have a question about subbundles of tangent bundles. If i have a subbundle E of TM and a local frame $\displaystyle X_1,..,X_n$ of TM ,s.t. $\displaystyle X_1,..,X_{n-q}$ is a local frame of E.

Is it right, that the dual frame $\displaystyle w_1,...,w_n$ of TM* has the property that $\displaystyle w_1,....,w_{n-q}$ forms a frame for E*?

Thank you.