Random Noise Generation

If P is a covariance then P is positive semi definite and P = T’ ΛT with T orthogonal and λ i ≥ 0. The n-dimensional Gaussian integral is defined and the normalization satisfies $${\left( {2\pi } \right)^{n/2}}{\left| P \right|^{1/2}} = \int {{e^{ - 1/2\left\| {x - \mu } \right\|_{p - 1}^2}}} dx$$ $$ = {\left( {2\pi } \right)^{n/2}}{\left( {{\lambda _1} \cdots {\lambda _n}} \right)^{1/2}}$$