Given 2n distinct real numers $s_1,s_2, \dots, s_n$ and $t_1, t_2, \dots,t_n$ define the $n \times n$ Cauchy matrix $C = C(t,s)$ by $C_{ij} = \frac{1}{t_i - s_j}$. Express the Lagrange interpolation formula: $$p(t_i) = \sum_{j=1}^{n}L_j(t_i)f_j$$ where $$L_j(t) = \prod_{k \neq j}\frac{t-s_k}{t_j - s_k}$$ in term of Cauchy matrix?
Can someone please explain to me how to express those term in Cauchy matrix ? Thank you