Abstract
In this paper, we consider the matrix whose -th entry is and compute its rank and a basis for its kernel (viewed as a matrix over the real numbers) when is prime. We also give a conjecture on the rank of this matrix when 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.
Citation
Maria I. Bueno. Susana Furtado. Jennifer Karkoska. Kyanne Mayfield. Robert Samalis. Adam Telatovich. "The kernel of the matrix $\lbrack i\mskip-2mu j \pmod n\rbrack$ when $n$ is prime." Involve 9 (2) 265 - 280, 2016. https://doi.org/10.2140/involve.2016.9.265
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