How to change state space from higher dimension to lower?

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I found the below text in a textbook. Can someone help in derivation
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Mario Malic
Mario Malic 2020-7-26
I am not sure if this is the space for such questions.
But you know a rule of matrix multiplication such as A*A^(-1)= I and it matters from which side you do the multiplication. Should be enough to start something.
Waqar Ahmed
Waqar Ahmed 2020-7-26
Actually these are the state space realizations matrices of transfer function. H(s)=C*(s*E-A)^-1*B+D. The transfer function is needed to derive these expressions

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