# Eigenvalues of a particular matrix

Given two vectors $\boldsymbol\alpha=\left(\alpha_1,...,\alpha_N\right)$ and $\boldsymbol\beta=\left(\beta_1,...,\beta_N\right)$, is there an easy way to compute the eigenvalues of a matrix $M_{k,q}$ whose entries are expressed as

$$M_{k,q}=\frac{\alpha_k}{\beta_q},\quad k=1,...,N,\quad q=1,...,N\quad ?$$

-

Hint: $M$ has rank $1$, and $M {\bf \alpha}^T = \ldots$