On Cullis’ determinant for rectangular matrices

We identify the column vectors of an n × k matrix (k ⩽ n) with a k-tuple of vectors in the n   dimensional vector space CnCn. The value of the alternative k-multiple linear functional D on the vector space of all n × k   matrices is uniquely determined by the value on the finite subset {(ei1,…,eik)∣i1<⋯