  Let $p$ be an odd prime number, and let $E$ be an elliptic curve defined over
a number field which has good reduction at every prime above $p$. Under
suitable assumptions, we prove that the $\eta$-eigenspace and the
$\bar{\eta}$-eigenspace of mixed signed Selmer group of the elliptic curve are
pseudo-isomorphic. As a corollary, we show that the $\eta$-eigenspace is
trivial if and only if the $\bar{\eta}$-eigenspace is trivial. Our results can
be thought as a reflection principle which relate an Iwasawa module in a given
eigenspace with another Iwasawa module in a "reflected" eigenspace.
