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

**Answer**

A covariance matrix C is called *isotropic*, or *spherical*, if it is proportionate to the identity matrix: C=λI, 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 V, then the covariance matrix will transform into V⊤CV=V⊤⋅λI⋅V=V⊤V⋅λI=λI, i.e. will stay the same.

Intuitively, isotropic covariance matrix corresponds to a “spherical” data cloud. A sphere remains a sphere after rotation.

**Attribution***Source : Link , Question Author : test , Answer Author : amoeba*