Abstract This paper considers the conjecture that given a real nonsingular matrix A, there exist a real diagonal matrix Λ with ¦λ ii λ = 1 and a permutation matrix P such that (ΛPA) is positive stable. The conjecture is shown to be true for matrices of order 3 or less and may not be true for higher order matrices. A counterexample is presented in terms of a matrix of order 65. In showing this, an interesting matrix Ml of order 2l = 64, which satisfies the matrix equation 2l-1(Ml + MTl), has been used. The stability analysis is done by first decomposing the nonsingular matrix into its polar form. Some interesting results are presented in the study of eigenvalues of a product of orthogonal matrices. A simple function is derived in terms of these orthogonal matrices, which traces a hysteresis loop.
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