Isotropic Gaussian

Definition

A random vector 𝑥∈ℝ^𝑑 follows an isotropic Gaussian if:

• $x\sim \mathcal{N}(0,{\sigma }^{2}I)$

where:

• mean = 0
• covariance = 𝜎²𝐼 (a scalar times the identity matrix = covariance matrix)
• all dimensions have the same variance
• all dimensions are uncorrelated