In this paper, we discuss foe characteristic matrices and similarity of timevarying linear differential systems with emphasis on the relationship of similarityand characteristic matrices of the systems, obtaining the necessary and sufficientcondition for a matrix bein characteristic matrix, the necessary and sufficientcondition for time-varying linear systems being similar and the necessary andsufficient condition for a time-varying linear system being similar to a blockdiagonai system. We improve one of t,he main results of [4].
