I want to generate correlation matrix such that it follows the below structure $$\Sigma = B \Lambda B^T $$
where $\Lambda$ is a diagonal matrix containing positive elements, $\Sigma \in R^{n \times n}$ is a correlation matrix and $B \in R^{n \times k}$ where $k$ is less than $n$. Here each column of $B$ is a sparse column with a certain sparsity $\lambda$ and $B$ is not necessarily orthogonal matrix. I am not sure how to generate a correlation matrix given above structure.
