A note on spectral norms of even-order r-circulant matrices

In this paper, we preset some improved techniques for proofs within Zhou and Jiang (2014). Meanwhile, focusing on n and r are co-prime, we generalize those results to investigate formulae of even-order r-circulant matrices with alternately positive and negative entrywise. And we deduce explicit formulae for their spectral norms with the entries in the first row.