In this manuscript, by defining the notion of \(\mathcal {A}^\lambda\) -matrix via the strictly increasing sequence \(\lambda =(\lambda _r)\) of positive reals tending to infinity, the spaces \(\mathcal {A}^\lambda (\ell _1)\) and \(\mathcal {A}^\lambda (bv)\) are defined as the domain of \(\mathcal {A}^\lambda\) -matrix in the sequence spaces \(\ell _1\) and bv, respectively. Additionally, investigations have been made for computing their topological properties, and certain inclusion relations are established. Furthermore, we determine algebraic dual, \(\alpha -, \beta -\) and \(\gamma -\) duals and examine the Schauder basis of the new spaces. In the end, certain matrix mappings between the new described sequence spaces are given, and the characterizations of some other classes are also derived from these results.
