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 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.

This article studies the constrained switching (linear) system which is a discrete-time switched linear whose sequences are by deterministic finite automaton. The stability of characterized its joint spectral radius that known to be difficult compute or approximate. Using semitensor product matrices, matrix-form expression shown equivalent lifted arbitrary system. Then, joint/generalized proven...

We give lower bounds on the size and total of clique partitions a graph in terms its spectral radius minimum degree, derive upper bound for maximum number edge-disjoint $t$-cliques. The extremal graphs attaining are exactly block Steiner $2$-designs regular with $K_t$-decompositions, respectively.