The relationship between the eigenvalues and eigenvectors of a similarity matrix and its associated Carbó index matrix

The eigenvalues and eigenvectors of a quantum similarity matrix are also generalized eigenvalues and eigenvectors of the associated matrix of Carbó indices. This establishes bounds on the spectrum of the Carbó index matrix; for example, a quantum similarity matrix is positive semidefinite if and only if the associated Carbó index matrix is also positive semidefinite. The generalized eigenvalue problem for the Carbó index matrix has a diagonal …