sentences:  Discretization formula_27 of the body of the scatterer formula_28 into formula_29 subdomains as formula_30 and using a set of linearly independent piece-wise continuous functions formula_31, formula_32, allows current density formula_33 to be represented as
  
  and by applying the Galerkin method, the impedance operator (2)
  
  The eigenvalue problem (1) is then recast into its matrix form
  
  which can easily be solved using, e.g., the generalized Schur decomposition or the implicitly restarted Arnoldi method yielding a finite set of expansion coefficients formula_37 and associated characteristic numbers formula_26.The properties of the CM decomposition are investigated below.The properties of CM decomposition are demonstrated in its matrix form.