Let $X\sim MVN(0,\Sigma)$ denote a random vector having the multivariate normal distribution with mean $0$ and covariance matrix $\Sigma$.
Suppose we want to sample from $X\sim MVN(0,\Sigma)$. Because $\Sigma$ is a positive semi-definite matrix (as it is a covariance matrix), there exists some matrix, $L$, such that $$\Sigma=LL',$$ where $L'$ is the transpose of $L$.
Observe now that we can write $𝑋 = 𝐿𝑌$, where $Y\sim MVN(0,I)$, where $I$ is the identity matrix.
Question: How to show the bolded equation? In particular, $X= LY$.