I am trying to simulate an autoregressive model such that $\mathbf{W}^t = \mathbf{W}^{t-1}\mathbf{M}$ where $\mathbf{M} \in \mathbb{R}^{k \times k}$ and $\mathbf{W} \in \mathbb{R}^{p \times k}$ where $p > k$. Also, squared $\ell2$ norm of each row of $\mathbf{W}$ matrix is $1$ Would it possible to sample $\mathbf{M}$ such that $\ell2$ norm of each row of $\mathbf{W}$ matrix is $1$?
Edit 1: I am thinking of using optimization to solve it by writing $p$ constrained equations where equation corresponds to the constraint that squared $\ell2$ norm of each row of $\mathbf{W}$ matrix is $1$. This will be overdetermined system of equations. Is there a simpler solution to it?