>>11282607In the simplest case, take , where the bilinear form is the usual dot product. We customarily write elements of as column matrices. Then elements of the dual space are written as row matrices. Going from one space to the other amounts to taking the transpose.
In general, this is not as simple, as the components of a covector are given as linear combinations of the components of the corresponding vector. In finite dimensional vector spaces, this can all be done with matrix computations.
