Summary: Let \(A = (a_{n,k})_{n,k\geq 1}\) and \(B = (b_{n,k})_{n,k\geq 1}\) be two non-negative matrices. Denote by \(L_{v,p,q,B}(A)\), the supremum of those \(L\), satisfying the following inequality:
\[ \|Ax\|_{v,B(q)}\geq L \| x\|_{v,B(p)}, \]
where \(x\geq 0\) and \(x\in l_p(v,B)\) and also \(v = (v_n)_{n=1}^\infty\) is an increasing, non-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for \(L_{v,p,q,B}(H_\mu)\), where \(H_\mu\) is the Hausdorff matrix and \(0 < q \leq p\leq 1\). Also for the case \(p = 1\), we obtain \(\|A\|_{w,B(1)}\), and for the case \(p\geq 1\), we obtain \(L_{w,B(p)}(A)\).