Radix-rational sequences are solutions of systems of recurrence equations based on the radix representation of the index. For each radix-rational sequence with complex values we provide an asymptotic expansion, essentially in the scale N logN . The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence of first-order differences. ...

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

We examine a special case of an approximation the joint spectral radius given by Blondel and Nesterov, which we call outer radius. The is square root ordinary n2 matrix $$\sum \overline {{X_i}} \otimes {X_i}$$ ∑ X i ¯ ⊗ . give analogue formula for can be used to quickly obtain error bounds in methods based on work Nesterov. analyze iterates completely positive map, including quantum channels. a...

We present an upper and a lower bound for the spectral radius of non-negative matrices. Then we give the bounds for the spectral radius of digraphs.