On the class of strictly isospectral systems

Two linear systems are called strictly isospectral if they share the same Jordan matrix. This paper provides some basic results on the class of all strictly isospectral systems. A key feature of this note is to show that this class consists of systems with various dimensions and orders. It is explained how this class can be generated from any given member without explicit knowledge of the spectral quantities. Some consequences for the corresponding equations of motion are discussed.