Solving linear systems via Pfaffians

Abstract

An explicit solution is given for the system of linear equations EφE^t=φ′, where φ,φ′ are alternating matrices of Pfaffian 1, which at most differ in their first row and column, and EE is of the form ∏_i=2^2rE_1i(x_i). If v,v′, w∈R^r+1 with 〈v,w〉=1=〈v′,w〉 then a sequence of Cohn transforms with respect to (the fixed) w which takes (v,w) to (v′,w) is prescribed.