  In this article, we propose a bivariate polynomial interpolation problem for
matrices (BVPIPM), for real matrices of the order $m\times n$. In the process
of solving the proposed problem, we establish the existence of a class of
$mn$-dimensional bivariate polynomial subspaces (BVPS) in which the BVPIPM
always posses a unique solution. Two formulas are presented to construct the
respective polynomial maps from the space of real matrices of the order
$m\times n$ to two of the particular established BVPS, which satisfy the
BVPIPM, by introducing an approach of bivariate polynomial interpolation.
Further, we prove that these polynomial maps are isomorphisms. Some numerical
examples are also provided to validate and show the applicability of our
theoretical findings.
