  The Leggett-Garg Inequality (LGI) constrains, under certain fundamental
assumptions, the correlations between measurements of a quantity Q at different
times. Here we analyze the LGI, and propose similar but somewhat more elaborate
inequalities, employing a technique that utilizes the mathematical properties
of correlation matrices, which was recently proposed in the context of nonlocal
correlations. We also find that this technique can be applied to inequalities
that combine correlations between different times (as in LGI) and correlations
between different locations (as in Bell inequalities). All the proposed bounds
include additional correlations compared to the original ones and also lead to
a particular form of complementarity. A possible experimental realization and
some applications are briefly discussed.
