Let x be a gaussian microx cx random vector let y ax

Question

Let X be a Gaussian (µ_X, C_X) random vector. Let Y = AX where A is an m ×n matrix of rank m. By Theorem 5.16, Y is a Gaussian random vector. Is a Gaussian random vector?

Theorem 5.16

Given an n-dimensional Gaussian random vector X with expected valueµ X and covariance CX, and an m × n matrix A with rank(A) = m,

Is an m-dimensional Gaussian random vector with expected value µ_Y = Aµ_X + b and covariance CY = AC_XA'