  Recently, in [1], the author proved that many results that are true for PPT
matrices also hold for another class of matrices with a certain symmetry in
their Hermitian Schmidt decompositions. These matrices were called SPC in [1]
(definition 1.1). Before that, in [9], T\'oth and G\"uhne proved that if a
state is symmetric then it is PPT if and only if it is SPC. A natural question
appeared: What is the connection between SPC matrices and PPT matrices? Is
every SPC matrix PPT?
  Here we show that every SPC matrix is PPT in $M_2\otimes M_2$ (theorem 4.3).
This theorem is a consequence of the fact that every density matrix in
$M_2\otimes M_m$, with tensor rank smaller or equal to 3, is separable (theorem
3.2). This theorem is a generalization of the same result found in [1] for
tensor rank 2 matrices in $M_k\otimes M_m$. Although, in $M_3\otimes M_3$,
there exists a SPC matrix with tensor rank 3 that is not PPT (proposition 5.2).
We shall also provide a non trivial example of a family of matrices in
$M_k\otimes M_k$, in which both, the SPC and PPT properties, are equivalent
(proposition 6.2). Within this family, there exists a non trivial subfamily in
which the SPC property is equivalent to separability (proposition 6.4).
