Abstract (EN):
In this paper, we consider the n×n matrix whose (i,j)-th entry is ij(modn) and compute its rank and a basis for its kernel (viewed as a matrix over the real numbers) when n is prime. We also give a conjecture on the rank of this matrix when n is not prime and give a set of vectors in its kernel, which is a basis if the conjecture is true. Finally, we include an application of this problem to number theory.
Type (Professor's evaluation):
Scientific