# What is an isotropic (spherical) covariance matrix?

Could somebody explain to me in simple terms what an isotropic covariance matrix is? I can’t find anything online.

A covariance matrix $\mathbf C$ is called isotropic, or spherical, if it is proportionate to the identity matrix: i.e. it is diagonal and all elements on the diagonal are equal.
This definition does not depend on the coordinate system; if we rotate coordinate system with an orthogonal rotation matrix $\mathbf V$, then the covariance matrix will transform into i.e. will stay the same.