A generalization of Sourourʹs theorem Original Research Article

LetX be an invertiblen × n matrix,n > 1, with entries in some fieldK. AssumeX ≠ diag(a, … a) for anya ε K. Then for every sequence (a1, …, an−1),ai ε K, there is a matrixY with entries in K and detY = 1 such that then − 1 principal minors ofYXY−1 have the valuesa1,… an−1), respectively. This generalizes Sourourʹ theorem, whereai ≠ 0 is assumed for alli.