Poincare matrix is $ M^{\mu\nu}$ in Poincare algebra which describes Lorentz transformations. You can look up wikipedia page https://en.wikipedia.org/wiki/Poincaré_group. If we write $ M^{\mu\nu}$ as matrix form, it looks like
$$ M^{\mu\nu}=\begin{pmatrix} 0 & -K_x & -K_y & -K_z \\ K_x & 0 &...