  We examine relationships between two minors of order n of some matrices of n
rows and n+r columns. This is done through a class of determinants, here called
$n$-determinants, the investigation of which is our objective. We prove that
1-determinants are the upper Hessenberg determinants. In particular, we state
several 1-determinants each of which equals a Fibonacci number. We also derive
relationships among terms of sequences defined by the same recurrence equation
independently of the initial conditions. A result generalizing the formula for
the product of two determinants is obtained. Finally, we prove that the Schur
functions may be expressed as $n$-determinants.
