  Properties of solutions of the RPA equation is reanalyzed mathematically,
which is defined as a generalized eigenvalue problem of the stability matrix
$\mathsf{S}$ with the norm matrix $\mathsf{N}=\mathrm{diag.}(1,-1)$. As well as
physical solutions, unphysical solutions are examined in detail, with taking
the possibility of Jordan blocks of the matrix $\mathsf{N\,S}$ into
consideration. Two types of duality of eigenvectors and basis vectors of the
Jordan blocks are pointed out and explored, which disclose many basic
properties of the RPA solutions.
