A bijective proof of Borchardt's identity
Summary: We prove Borchardt's identity \[ \text{det}\Biggl({1\over x_i- y_j}\Biggr)\text{per}\Biggl({1\over x_i- y_j}\Biggr)= \text{det}\Biggl({1\over (x_i- y_j)^2}\Biggr) \] by means of sign-reversing involutions.
scientific article; zbMATH DE number 2107490