Question: Show that the transfer function of a given digital filter is invariant with respect to a linear transformation of the state vector [mathbf{x}(n)=mathbf{T} mathbf{x}^{prime}(n)] where

Show that the transfer function of a given digital filter is invariant with respect to a linear transformation of the state vector

\[\mathbf{x}(n)=\mathbf{T} \mathbf{x}^{\prime}(n)\]

where \(\mathbf{T}\) is any \(N \times N\) nonsingular matrix.

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