First and second order characterizations of pseudolinear functions

Abstract This work is concerned with first and second order characterizations of pseudolinear functions. It is shown that for continuously differentiable function δφ ( x ) ≠ 0, pseudolinearity is completely characterized by a special property of the normalized gradient δφ ( x ) / | δφ ( x )|. Applying some results on the quasi-Hessian matrices the eigenvalues and the eigenvectors of the Hessian Δ 2 φ ( X ) of a twice continuously differentiable pseudolinear function φ ( x ) is characterized.