  Let $R$ be a Hermitian matrix. The energy of $R$, $\mathcal{E}(R)$,
corresponds to the sum of the absolute values of its eigenvalues. In this work
it is obtained two lower bounds for $\mathcal{E}(R).$ The first one generalizes
a lower bound obtained by Mc Clellands for the energy of graphs in $1971$ to
the case of Hermitian matrices and graphs with a given nullity. The second one
generalizes a lower bound obtained by K. Das, S. A. Mojallal and I. Gutman in
2013 to symmetric non-negative matrices and graphs with a given nullity. The
equality cases are discussed. These lower bounds are obtained for graphs with
$m$ edges and some examples are provided showing that, some obtained bounds are
incomparable with the known lower bound for the energy $2\sqrt{m}$. Another
family of lower bounds are obtained from an increasing sequence of lower bounds
for the spectral radius of a graph. The bounds are stated for singular and
non-singular graphs.
