of multiplicative terms $\{M_{ik}, i \in \fromto{0}{m}, k \in [d]\}$ of parameter matrices $\sth{g_{t,1}^b, g_{t,2}^b}$ and constant matrices $\sth{W_{t,1}^b, W_{t,2}^b, W_1^*, W_2^*}$ such that $$\begin{aligned}
                \prod_{i=1}^m \trace{M_i} M_0 = \sum_{k=1}^{d} \prod_{i=1}^{m} \trace{M_{ik}} M_{0k},
            \end{aligned}$$ where $\sum_{i=0}^m \deg\pth{M_{ik}} \le d$.

With the help of Lemmas \[lemma:GtoW\] and \[lemma:WtoG\], we can represent $g_{t,i}^b, i=1,2$ using multiplicative terms of $g_{t-1,i}^b, i=1,2$ and some other constant matrices. Furthermore, by iteratively reducing the value of $t$, we are able to represent $g_{t,i}^b, i=1,2$ by the variables in $t = 0$. Theorem \[thm:representation\] precisely gives the representation in the form of a polynomial of $\frac{1}{b}$ and the coefficients as the sum of multiplicative terms of parameter matrices $\sth{W_{0,1}^b, W_{0,2}^b}$ and constant matrices $\sth{W_1^*, W_2^*}$.

\[thm:representation\] Given $t \ge 0$, for any multiplicative terms $M_i, i \in \fromto{0}{m} $ of parameter matrices $\left\{ g_{t,1}^b, g_{t,2}^b \right\}$ and constant matrices $\sth{W_{t,1}^b, W_{t,2}^b, W_1^*, W_2^*}$ with degree $d_i$, respectively, we denote $M = \prod_{i=1}^m \trace{M_i} M_0$, $d = \sum_{i=0}^m d_i$ and $d' = \sum_{i=0}^m \pth{\deg\pth{W_{t,1}^b; M_i} + \deg(W_{t,2}^b; M_i)}$. There exists a set of multiplicative terms $\sth{M_{ij}^k, i\in [m_k], j \in \fromto{0}{m_{ki}}, k \in \fromto{0}{q}}$ of parameter matrices $\sth{W_{0,1}^b, W_{0,2}^b}$ and constant matrices $\sth{W_1^*, W_2^*}$ such that $$\begin{aligned}
                \condexp{}{M}{\calF_0} 