Paraphrase the following text using more academic and scientific language Use a neutral tone and avoid repetitions of words and phrases对$Cn^n^$中的算符进行表象变换并插入完备性条件$Cn^n^$可以扩展为

By performing a unitary transformation on the operators in $C(n^{'},n^{''})$ and inserting the completeness condition, $C(n^{'},n^{''})$ can be expanded into a more comprehensive form.