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- Bounded domains of negative multipliersPublication . Johnson, Charles; Morais, GonçaloA natural problem associated with coupling of non-autonomous oscillators and synchronization is described. It leads to a question about the boundedness of a domain associated with a derived quadratic form. Properties of real symmetric matrices with bounded domains are developed, and unboundedness is translated into satisfiability of a certain Lyapunov-like matrix form. Eventually the real symmetric matrices associated with unbounded domains are explicitly characterized in terms of inertia explicit matrices. A consequence of the characterization is that large, irreducible matrices are likely to have bounded domains.