  We present the $W_{1+\infty}$ constraints for the Gaussian Hermitian matrix
model, where the constructed constraint operators yield the $W_{1+\infty}$
$n$-algebra. For the Virasoro constraints, we note that the constraint
operators give the null 3-algebra. With the help of our Virasoro constraints,
we derive a new effective formula for correlators in the Gaussian Hermitian
matrix model.
