# How do I invert this matrix?

Given two vectors $$\vec{v} = \begin{pmatrix} v_1\\ \vdots\\ v_n \end{pmatrix} , \vec{w} = \begin{pmatrix} w_1\\ \vdots\\ w_n \end{pmatrix} \in \mathbb{R}^n$$

such that for all $$1 \leq j, k \leq n$$

• $$v_j \neq v_k$$ for $$j \neq k$$
• $$w_j \neq w_k$$ for $$j \neq k$$
• $$v_j \neq w_k$$
• $$v_j >0 \quad$$
• $$w_j >0 \quad$$

Define a Matrix $$A \in \mathbb{R^{n \times n}}$$ with entries $$a_{jk}$$, for $$1 \leq j, k \leq n$$, by

$$a_{j k} :=\frac{1}{(v_j - w_k)^2}$$

Is there any simple way to get an expression for its inverse? I'm really a newbie in linear algebra, this object seems simple enough to be already known, but I can't solve this nor find it solved anywhere.