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todays session is about similarity transformations let us assume that we have a vector X given by one so let us assume another matrix a equal to two three four five let us assume a linear transformation X bar equal to a X this results in two three four five multiplied by one so this will result in basically a similarity transformation or a linear transformation results in converting one column vector into another this idea is used in conversion of one state model to another let us move on to the actual topic here we discuss conversion from one state model to another using similarity transformation while discussing state models we have seen three different types of state models like controllable canonical form observable canonical form diagonal canonical form and a subset of this is northern canonical form and we have also seen physical state models which do not belong to any of the above-mentioned canonical forms like state models for an RLC circuit with physical variables as state v