So I have a definition for each of the above:

**Eigenbasis**: when the matrix in question is in diagonal form. Only possible when there are n eigenvectors for a matrix in n-dimensional space.

**Orthonormal basis**: when basis vectors are a)orthogonal, b)unit-length. 

What I'm trying to understand is - how do they relate? Like, is eigenbasis always orthonormal? Or does orthonormal basis always have an eigenbasis? Or are the two the same even?

Thanks!