I've been trying to rewrite the matrix $\left( \begin{array}{cccc} x_{n} & x_{1} & x_{2} & \cdots & x_{n-1} \\ x_{1} & x_{n} & 0 &\cdots & 0 \\ x_{2} & 0& \ddots & 0 & \vdots\\ \vdots & \vdots& & \ddots \\ x_{n-1} & 0 & \cdots & & x_{n} \end{array} \right) $
into the form $-A_{0}+\sum_{k=1}^{n}A_{k}x_{k}$ for matrices $A_{k}$ and scalars $x_{k}$.
Could anyone help me with this?
The main problem I have is that $\sum_{k=1}^{n}A_{k}x_{k}$ gives a vector and im suppose to add this to the matrix $-A_{0}$? How does one add a vector to a matrix in this context?