  In the present paper, we introduce the notion of $E$-$g$-frames for a
separable Hilbert spaces $\mathcal H$, where $E$ is an invertible infinite
matrix mapping on the Hilbert space
$\mathop\oplus\limits_{n=1}^{\infty}\mathcal H_n$. We study some prperties of
$E$-$g$-frames. First, we give a result concerning perturbation of
$E$-$g$-frames and then use it to construct $E$-$g$-frames in separable Hilbert
spaces.
