# Does this special matrix have a name?

I encountered a matrix of the following form:

\begin{pmatrix} 1 & 1 & \cdots & 1 & 1 \\ x_1 & x_2 & \cdots & x_{n-1} & x_n \\ \vdots & \vdots & & \vdots & \vdots \\ x_1^{n-2} & x_2^{n-2} & \cdots & x_{n-1}^{n-2} & x_n^{n-2} \\ x_1^{n-1} & x_2^{n-1} & \cdots & x_{n-1}^{n-1} & x_n^{n-1} \end{pmatrix}

or, by multiplying the above matrix with $(x_1,x_2,\ldots,x_{n-1},x_n)^T$:

\begin{pmatrix} x_1 & x_2 & \cdots & x_{n-1} & x_n \\ x_1^2 & x_2^2 & \cdots & x_{n-1}^2 & x_n^2 \\ \vdots & \vdots & & \vdots & \vdots \\ x_1^{n-1} & x_2^{n-1} & \cdots & x_{n-1}^{n-1} & x_n^{n-1} \\ x_1^n & x_2^n & \cdots & x_{n-1}^n & x_n^n \end{pmatrix}

I was wondering if this type of matrix has a name?

Best regards.

• Vandermonde matrix – Wuestenfux May 19 '17 at 8:41

Vandermonde Matrices. But you won't get the second matrix by multiplying $(x_1,x_2,x_3,\dots,x_n)'$ to the first matrix.
• Ah yes, you are right. I meant a diagonal matrix with $x_1$,...,$x_n$ as diagonal values. Thanks! – Prashant Jun 21 '17 at 8:48