Some Gr\"{u}ss type inequalities for $n$-tuples of vectors in semi-inner modules

Some Gr"{u}ss type inequalities in semi-inner product modules over $C^{\ast }$-algebras and $H^{\ast }$-algebras for $n$-tuples of vectors are established. Also we give their natural applications for the approximation of the discrete Fourier and the Melin transforms in such modules.