  The Lax representation for different matrix generalizations of Short Pulse
Equations (SPE) is considered. The four-dimensional Lax representations of
four-component Matsuno, Feng and Dimakis-M\"{u}ller-Hoissen-Matsuno equations
is obtained. The four-component Feng system is defined by generalization of the
two-dimensional Lax representation to the four-component case. This system
reduces to the original Feng equation or to the two-component Matsuno equation
or to the Yao-Zang equation. The three component version of Feng equation is
presented.
  The four-component version of Matsuno equation with its Lax representation is
given .
  This equation reduces the new two-component Feng system.
  The two-component Dimakis-M\"{u}ller-Hoissen-Matsuno equations are
generalized to the four parameter family of the four-component SPE. The
bi-Hamiltonian structure of this generalization, for special values of
parameters, is defined. This four-component SPE in special case reduces to the
new two-component SPE.
