: Mathématiques: Vandermonde matrix

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Vandermonde matrix

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 ${\\displaystyle (m+1)\ imes (n+1)}$ matrix
${\\displaystyle V=V(x_{0},x_{1},\\cdots ,x_{m})={\egin{bmatrix}1&x_{0}&x_{0}^{2}&\\dots &x_{0}^{n}\\\\1&x_{1}&x_{1}^{2}&\\dots &x_{1}^{n}\\\\1&x_{2}&x_{2}^{2}&\\dots &x_{2}^{n}\\\\\\vdots &\\vdots &\\vdots &\\ddots &\\vdots \\\\1&x_{m}&x_{m}^{2}&\\dots &x_{m}^{n}\\end{bmatrix}}}$
with entries ${\\displaystyle V_{i,j}=x_{i}^{j}}$ , the j^th power of the number ${\\displaystyle x_{i}}$ , for all zero-based indices ${\\displaystyle i}$ and ${\\displaystyle j}$ . Most authors define the Vandermonde matrix as the transpose of the above matrix
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Vandermonde_matrix)