Table 2 Euclidean norms of \(\pmb{C_{r}^{(k)}}\) for \(\pmb{n=5}\)
From: On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers
k / r | k = 1 | k = 2 | k = 3 | k = 4 |
|---|---|---|---|---|
r = −2 | \(\frac{\sqrt{9{,}935}}{6}\) | \(\frac{\sqrt{61{,}598}}{6}\) | \(\frac{ \sqrt{246{,}743}}{6}\) | \(\frac{\sqrt{755{,}966}}{6}\) |
r = −0.5 | \(\frac{\sqrt{7{,}415}}{12}\) | \(\frac{\sqrt{37{,}127}}{12}\) | \(\frac{\sqrt{136{,}007}}{12}\) | \(\frac{\sqrt{397{,}559}}{12}\) |
r = 0.1 | \(\frac{\sqrt{133{,}655}}{60}\) | \(\frac{\sqrt{593{,}351}}{60}\) | \(\frac{\sqrt{2{,}038{,}631}}{60}\) | \(\frac{\sqrt{5{,}736{,}887}}{60}\) |
r = 0.9 | \(\frac{\sqrt{306{,}055}}{60}\) | \(\frac{\sqrt{1{,}709{,}431}}{60}\) | \(\frac{\sqrt{6{,}577{,}111}}{60}\) | \(\frac{\sqrt{19{,}743{,}847}}{60}\) |
r = 1 | \(\frac{\sqrt{3{,}470}}{6}\) | \(\frac{\sqrt{19{,}745}}{6}\) | \(\frac{5 \sqrt{3{,}062}}{6}\) | \(\frac{\sqrt{230{,}705}}{6}\) |
r = 1.1 | \(\frac{\sqrt{392{,}255}}{60}\) | \(\frac{\sqrt{2{,}267{,}471}}{60}\) | \(\frac{\sqrt{8{,}846{,}351}}{60}\) | \(\frac{\sqrt{26{,}747{,}327}}{60}\) |
r = 10 | \(\frac{\sqrt{216{,}815}}{6}\) | \(\frac{\sqrt{1{,}400{,}894}}{6}\) | \(\frac{\sqrt{5{,}692{,}919}}{6}\) | \(\frac{\sqrt{17{,}564{,}318}}{6}\) |