In this paper, the $mn$-dimensional space of tensor-product polynomials of two variables, of degree at most $(m-1)+(n-1)$, is considered. A theory of two-variate polynomials is developed by establishing the algebra and basic algebraic properties with respect to the usual addition, scalar multiplication, and a newly defined algebraic operation in the considered space. Further, the existence of the considered space is established with respect to the matrix interpolation problem (MIP), $P(i,j)=a_{ij}$ for all $1 \leq i \leq m$, $1 \leq j \leq n$, corresponds to a given matrix $(a_{ij})_{m \times n}$ in the space of $m \times n$ order real matrices. The poisedness of the MIP is proved and three formulae are presented to construct the respective polynomial in the considered space. After that, using construction formulae, a polynomial map from the space of $m \times n$ order real matrices to the considered space is defined. Some properties of the polynomial map are investigated and some isom 查看全文>>