This study characterizes the bicomplex matrix transformations \(\left( \ell _{\infty }\left( \mathbb{B}\mathbb{C}\right) ,c\left( \mathbb{B}\mathbb{C}\right) \right) \) and \(\left( \ell _{1}\left( \mathbb{B}\mathbb{C}\right) ,\ell _{p}\left( \mathbb{B}\mathbb{C} \right) \right) \) . Using the idempotent representation, we decompose bicomplex modules into complex components to establish necessary and sufficient conditions for these transformations. We present the \(\mathbb{B}\mathbb{C}\) -Schur theorem as a bicomplex analogue of the classical version and introduce the concept of \(\mathbb{B}\mathbb{C}\) -characteristic \(\chi \left( B\right) \) to examine the properties of \(\mathbb{B}\mathbb{C}\) -regular matrices. The results, supported by bicomplex Minkowski and Hölder inequalities, identify how structural constraints in the bicomplex setting modify classical summability conditions.
