The main purpose of this paper is to obtain solutions of matrix equations of the following types,
A
X
−
X
B
=
C
,
X
D
X
+
A
X
+
X
B
+
C
=
0
AX - XB = C,XDX + AX + XB + C = 0
, in which case
X
X
is an unknown
n
n
by
n
n
matrix and
A
,
B
,
C
,
D
A,B,C,D
are
n
n
by
n
n
matrices having elements belonging to the field
C
C
of complex numbers. Results obtained extend those of W. E. Roth, J. E. Potter and others concerning the existence and the representation of solutions
X
X
of the above equations.