# Deano

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 Jun17 accepted A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices Jun15 answered A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices May19 revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices deleted 272 characters in body May17 awarded Nice Question May17 comment A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices @user1551, it only happens for larger $n$ and very large $k$. Although, for $k$ which is relatively small to $n$, it does not exceed $3$ even for large $n$. It might have something to do with the accuracy of the "funm" function rather than to the result itself. I have no intuition as to why it should not be uniformly bounded. May16 comment A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices @StephenMontgomery-Smith, thank you for your comment. Trying to derive an analytic expression, even though the diagonalization is explicitly known, was not successful. However, I did try random symmtric stochastic circulant matrices in Matalb, and for $k = O(\log n)$ the results were indeed small. However, for larger $k$ (which I am not interested), the results did exceed $3$. Any other insight would be helpful, as I am trying to show that under some (maybe more) constraints I can bound the infinity norm of $\frac{1}{T}\sum_{k=1}^{T}\cos(kA)$ by a constant, for $T = O(\log n)$. May13 comment A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices @user1551, in case $A$ is the $2 \times 2$ matrix $[a,1-a;1-a, a]$, the infinity norm is given by $\max\{|\cos(k)|,|\cos((2a-1)k)|\}$. And indeed, as you stated, the maximum is obtained for $a=0.5$, which corresponds to your assumption. Unfortunately, I had no further insight. Thank you. May8 revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices alternative formulation May5 revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices added 4 characters in body May5 revised A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices added explainations May5 asked A sharper bound for $\|\cos(kA)\|_{\infty}$ for symmetric stochastic matrices Mar22 awarded Teacher Mar22 answered Asymptotics of Gelfand's formula Mar18 awarded Supporter Mar18 comment Asymptotics of Gelfand's formula Indeed, thank you. However, it did imply that there is a more concrete expression than the usual: $\forall \epsilon \exists N \forall k \ge N. \|A^k\| < (\rho(A)+\epsilon)^{k}$. Specifically, the relations between those constants. Are you aware of any? Mar18 revised Asymptotics of Gelfand's formula added 8 characters in body Mar18 revised Asymptotics of Gelfand's formula deleted 11 characters in body Mar18 asked Asymptotics of Gelfand's formula Feb25 comment Rate of convergence of Fourier series Of course, I will rephrase. Is there a result not involving the Lipschitz constant? Feb25 asked Rate of convergence of Fourier series