A counterexample to a conjecture of Friedland
The author studies a conjecture of \textit{S. Friedland} [Linear Algebra Appl. 192, 109--114 (1993; Zbl 0787.15011)] which says that ``if two symmetric matrices over the ring of integers are orthogonally similar over both the field of rationals and the ring of \(p\)-adic integers, then the two symmetric matrices should be orthogonally similar over the ring of integers''. A clever method for constructing counterexamples to the conjecture is provided. An explicit example is also given. Finally, the paper presents a modified version of the conjecture above, i.e., requiring that the characteristic polynomial of the matrices being irreducible over \(Q[x]\). The paper is well written and very readable.
scientific article; zbMATH DE number 5549258