DAEs and the Generalized Eigenvalue Problem

First we will consider three typical examples from [GL83]  

The corresponding eigenvalue problem has only one finite solution /x = 1, whereas the dimension of this problem is 2, It can easily be seen that the DAE is equivalent to the scalar ODE 

the eigenvalue problem has no solution at all and the DAE turns out to consist simply of two algebraic equations (no dynamics ) 

The eigenvalue problem can also take any complex number as solution. 

The properties of the generalized eigenvalues coincide with the classical case only if E is a regular matrix  

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