$$ \begin{array}{c} \text{Enter the dimensions } m \text{ (domain) and } n \text{ (image),} \\ \text{ generate the input fields, fill in the matrices, and compute the} \\ \text{matrix representation } \mathbf{B} = \mathbf{U}^{-1} \mathbf{A} \mathbf{V}, \\ \text{where } \mathbf{V} \text{ is the domain space (initial) basis matrix, } \\ \mathbf{U} \text{ is the image space (final) basis matrix, and } \\ \mathbf{A} \text{ is the matrix representation of the linear transformation in the standard basis.} \end{array} $$