In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row: an × {\displaystyle \times } matrix V = V = [ 1 x 0 x 0 2 … x 0 n 1 x 1 x 1 2 … x 1 n 1 x 2 x 2 2 … x 2 n ⋮ ⋮ ⋮ ⋱ ⋮ 1 x m x m 2 … x m n ] {\displaystyle V=V={\begin{bmatrix}1&x_{0}&x_{0}^{2}&\dots &x_{0}^{n}\\1&x_{1}&x_{1}^{2}&\dots &x_{1}^{n}\\1&x_{2}&x_{2}^{2}&\dots &x_{2}^{n}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&x_{m}&x_{m}^{2}&\dots &x_{m}^{n}\end{bmatrix}}} with entries V i, j = x i j {\displaystyle V_{i,j}=x_{i}^{j}}, the jth power of the number x i {\displaystyle x_{i}}, for all zero-based indices i {\displaystyle i} and j {\displaystyle j}. Wikipedia