Transforming multivariate $N(0,1)$ samples into $N(\mu,\sigma^2)$ samples via matrix operations
If $X$ is multivariate normal, any affine transform $AX+b$ is also multivariate normal for constants $A,b$. Thus,
$$Z\sim N(0,\mathbb{I}_n)\iff Z_i\overset{\text{i.i.d}}{\sim} N(0,1)\\ \implies Y\equiv \sigma Z+\mu{\bf1}_n\sim N(\mu{\bf1}_n, \sigma^2\mathbb{I}_n)\iff Y_i\overset{\text{i.i.d}}{\sim} N(\mu,\sigma^2),\ $$ where ${\bf1}_n$ is the $n\times 1$ column vector of ones.
Update: More generally, if $X\sim N(\mu_X,\Sigma_X)$, then $Y\equiv AX+b\sim N(A\mu_X+b,A\Sigma_XA').$