let $\mathbf{r}_p(u)=(1,u,u^2,\ldots,u^p)'\in\mathbb{R}^{1+p}$ and let $$\mathbf{R}_p = [\mathbf{r}_p(x_1), \mathbf{r}_p(x_2), \cdots, \mathbf{r}_p(x_n)]'_{n\times(1+p)}.$$ Moreover, let $\mathbf{Z}\in\mathbb{R}^n$. Is there any way to obtain the following matrix $$\begin{bmatrix}Z_1\mathbf{r}_p(x_1), Z_2\mathbf{r}_p(x_2), \cdots, Z_n\mathbf{r}_p(x_n)\end{bmatrix}'_{n\times(1+p)}$$ using matrix operations that involve $\mathbf{Z}$ and $\mathbf{R}_p$? The only one I've been able to obtain was $$(\mathbf{Z}\boldsymbol{\iota}_{1+p}')\odot \mathbf{R}_p,$$ where $\boldsymbol{\iota}_k$ is a $k\times 1$ vector of ones and $\odot$ denotes the Hadamard product. I'd like not to use the Hadamard product though, but it seems to me the only way to go.
Thanks a lot for your help!