# Simulate correlation matrix using a given structure

by Dushyant Sahoo   Last Updated November 09, 2018 01:19 AM

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.

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