Control Systems - Canonical Forms

Given an observable realization (A,b,c). Determine in terms of the matrices A,b, and c the similarity transfrom T, that brings the this system to the observability canonical form. Can this be done if (A,b,c) is not observable too?

I don't know where to start. I am thinking pick matrices(A,b,c) with arbitrary random values
or do I have to find first whether this system is observable? If the realization is observable isn't it already in the canonical form? Why the need for a similarity transform?
 

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