Decomposing Samuelson maps

AbstractA Samuelson map is here defined as a differentiable self-mapping of n-space with the property that the leading principal minors of its Jacobian matrix vanish nowhere. Structure theorems are proved for Samuelson maps that satisfy various simple conditions on the pivots arising from Gaussian elimination of the Jacobian matrix. The theorems yield representations of a Samuelson map as a (unique) composition of invertible maps that alter only a single coordinate