  While every matrix algebra over a field $K$ can be realized as a Leavitt path
algebra, this is not the case for every graded matrix algebra over a graded
field. We provide a complete description of graded matrix algebras over a
field, trivially graded by the ring of integers, which are graded isomorphic to
Leavitt path algebras. As a consequence, we show that there are graded corners
of Leavitt path algebras which are not graded isomorphic to Leavitt path
algebras. This contrasts a recent result stating that every corner of a Leavitt
path algebra of a finite graph is isomorphic to a Leavitt path algebra. If $R$
is a finite direct sum of graded matricial algebras over a trivially graded
field and over naturally graded fields of Laurent polynomials, we also present
conditions under which $R$ can be realized as a Leavitt path algebra.
