On the computational aspects of the theory of joint spectral radius

A study was conducted to analyze the computational aspects of the theory of joint spectral radius. Analyses revealed that one of the characteristics describing the exponential rate of growth of matrix products was the joint or generalized spectral radius. The study also focused on obtaining effective estimates for the theory of joint spectral radius by formulating a set of matrices with elements from the field real or complex numbers. The term A n was used to denote the set of all products of n matrices from A. It was informed in one of the equations that norms were replaced by positive homogeneous polynomials of even degree in the definition of joint spectral radius. Different explicit a priori estimates were obtained for the joint spectral radius of an irreducible set of matrices that were assumed to be more constructive.