Transformation of linear systems

K and K are assumed to be regular Jacobi matrices of two different linear systems of equal rank s. Furthermore, all eigenvalues are assumed to be different. Under these conditions, similarity transformations S and S are possible  

D and D are diagonal matrices. If all eigenvalues of K and K are equal, that means 

The transformation T is linear, if the primed system can be transformed into the non-primed system. In this case. 

The matrices K and K are similar matrices they have the same eigenvalues and principal minors [18]. 

One looks for the transformation T which transforms the system into the reaction 

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