When generating a multivariate normal distribution random number,
(1) firstly generating covariance matrix sigma; (2) and then generating covariance matrix sigma decomposition to determine the matrix root of sigma (decomposition methods such as eigenvalue decomposition, singular value decomposition, and Cholesky decomposition. I am not sure about this part. My teacher mentioned it very quickly in the class. I very appreciate if someone can explain this part further).
My question is: Why using decomposition instead of covariance matrix? When generating a normal distribution I remember we just use mean + sigma * rand directly. Thanks!
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