  We identify the rank $(q_{syk}+1)$ of the interaction of the two-dimensional
${\cal N}=(2,2)$ SYK model with the deformation parameter $\lambda$ in the
Bergshoeff, de Wit and Vasiliev(in 1991)'s linear $W_{\infty}[\lambda]$ algebra
via $\lambda =\frac{1}{2(q_{syk}+1)}$ by using a matrix generalization. At the
vanishing $\lambda$ (or the infinity limit of $q_{syk}$), the ${\cal N}=2$
supersymmetric linear $W_{\infty}^{N,N}[\lambda=0]$ algebra contains the matrix
version of known ${\cal N}=2$ $W_{\infty}$ algebra, as a subalgebra, by
realizing that the $N$-chiral multiplets and the $N$-Fermi multiplets in the
above SYK models play the role of the same number of $\beta\, \gamma$ and $b\,
c$ ghost systems in the linear $W_{\infty}^{N,N}[\lambda=0]$ algebra. For the
nonzero $\lambda$, we determine the complete ${\cal N}=2$ supersymmetric linear
$W_{\infty}^{N,N}[\lambda]$ algebra where the structure constants are given by
the linear combinations of two different generalized hypergeometric functions
having the $\lambda$ dependence. The weight-$1, \frac{1}{2}$ currents occur in
the right hand sides of this algebra and their structure constants have the
$\lambda$ factors. We also describe the $\lambda =\frac{1}{4}$ (or $q_{syk}=1$)
case in the truncated subalgebras by calculating the vanishing structure
constants.
