  In information theory, the well-known log-sum inequality is a fundamental
tool which indicates the non-negativity for the relative entropy. In this
article, we establish a set of inequalities which are similar to the log-sum
inequality involving two functions defined on scalars. The parametric extended
log-sum inequalities are shown. We extend these inequalities for the
commutative matrices. In addition, utilizing the L\"{o}wner partial order
relation and the Hansen-Pedersen theory for non-commutative positive
semi-definite matrices we demonstrate a number of matrix-inequalities analogous
to the log-sum inequality.
