Given a $n \times n$ real Cauchy like matrix $C$, i.e., for real vectors $r$, $s$, $x$, $y$ 


$$
C\_{ij} = \frac{r\_i s\_j}{ x\_i - y\_j}
$$



> 
> Can a Cauchy-like $C$ be orthogonal, i.e., $C C^T = I$ for $n > 2$?
> 
> 
> 


There exists such an orthogonal $C$ for $n = 2$ , $x = [1,0.4]$, $y = [6.25,0.625]$, $r = [-1.8114, 1.4811]$, and $s = [2.3367, -0.1225]$ with 


$$
C = \begin{bmatrix}
0.8062 & 0.5916 \\
-0.5916 & 0.8062
\end{bmatrix}
$$



Orthogonal Cauchy-like matrix
Please give a look at [this short note](https://www.researchgate.net/publication/341979812_Do_orthogonal_Cauchy-like_matrices_exist).


