The solvability conditions for the inverse eigenvalue problem of the symmetrizable matrices.
The authors investigate the inverse eigenvalue problem of finding a symmetrizable real matrix \(A\) that solves \(AX = X\Lambda\) for a given real matrix \(X\) and a given real diagonal matrix \(\Lambda\), as well as a related minimal norm approximation problem. The solution is found via the singular value decomposition (SVD) of a related matrix. Despite the paper's short and recent list of references, symmetrizable matrices have been studied for several centuries by Cauchy, Weierstraß, Kronecker, Frobenius, Taussky, Zassenhaus, Thompson among others, as well as by the reviewer. The basic theorems and lemmas of p. 102 are all well known and need no proof. One (Lemma 2.1) is erroneously attributed to a 1991 book in Chinese, while the SVD is laughably attributed to Golub and van Loan. These are unforgivable lapses of the Journal's editorial system. The authors' work is otherwise nice and deserved better editorial attention and care.
scientific article; zbMATH DE number 2055538