## Special Matrix (8) Vandermonde Matrix

Vandermonde matrices have the following form:$$A_n=\begin{bmatrix} 1&x_1&x_1^2&\cdots&x_1^{n-1}\\ 1&x_2&x_2^2&\cdots&x_2^{n-1}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ 1&x_n&x_n^2&\cdots&x_n^{n-1} \end{bmatrix},$$ where $A_n=[a_{ij}]_{i,j=1}^n$ is an $n\times n$ matrices and the element $a_{ij}=x_i^{j-1}$. The transpose $A_n^T$ is also called a Vandermonde…