Question on Matlab's ss2tf function

Hello, Looking at the function ss2tf - which converts state space to transfer function I am trying to understand how the numerator polynomial is
calculated. I understand how the denominator polynomial is calculated, but can't figure out how the numerator works out.
The numerator is calculated by: num = det(sI- A +BC) -det(sI-A)
note: A, B, C, D are the regular state space matrices (in this case D=0). So the numerator comes from the eigenvalues of the matrix A-BC and the matrix A
I would be grateful for hints in the derivation or a pointer to a paper.
Thanks. David
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It is all there in the Matlab code. Just
type ss2tf
and you'll see how.
--Nasser
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Looking at the ss2tf function was how I got the above function for the numerator. My question is how is it derived. Normally the transfer function is given as C inv(sI-A)B +D. Substituting the adjoint and determinant for the inverse allows you to determine the denominator polynomial. So how do you go from the above formula to the numerator polynomial?
Cheers, Dave
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