The problem of characterizing those linear systems that exhibit a symmetric behavior was completely solved in the 1D case, ten years ago, in a few papers by F. Fagnani and J. C. Willems. Unfortunately, that theory could not be extended in its full generality to multidimensional systems: the techniques used in the proofs limited the results to systems of independent equations and to a restricted...

Infrared spectroscopy studies of 1,3-indanedione (ID) in 16 different pure organic solvents were undertaken to investigate the solvent– solute interactions and to correlate solvent properties, such as the Kirkwood–Bauer–Magat (KBM) equation, the solvent acceptor number (AN) and the linear solvation energy relationships (LSER), using the infrared band shift. The correlations were performed both ...

For a matrix A = [aij ] m,n i,j=1 ∈ Fm×n, the transpose of A is the matrix A> = [aji] n,m j,i=1 ∈ Fn×m. A square matrix A ∈ Rn×n is called symmetric if aji = aij for all i, j ∈ {1, . . . , n} and is called skew-symmetric or anti-symmetric if aji = −aij for all i, j ∈ {1, . . . , n}. A basis will be denoted B = {u1,u2, . . . ,un} when the ordering of the basis vectors is not important and B = [u...