So we can diagonalize this matrix and get new single-electron eigenstates, replacing the orbitals we started with.    From Wordnik.com.  [Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask] Reference

Where A is the matrix you are attempting to diagonalize and I is the identity matrix of the same dimensions as A where A is square.    From Wordnik.com.  [The Euro Team and the SWM Network « Climate Audit] Reference