Majed Hamadi - Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
Nezam Mahdavi-Amiri - Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

Here we investigate the bounds for norm of matrix functions, considering theCrouzeix’s conjecture. We provide bounds for the norm of a matrix function using thenumerical range and Faber polynomials. In particular, we obtain bounds for norm ofthe sine and cosine and also the hyperbolic sine and cosine functions of matrices asexponential functions

Crouzeix’s conjecture, Numerical range, Matrix functions