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Sum of squares representation for the Böttcher-Wenzel biquadratic form. (English) Zbl 1311.90094
Summary: We find the minimum scale factor, for which the nonnegative Böttcher-Wenzel biquadratic form becomes a sum of squares (sos). To this we give the primal and dual solutions for the underlying semidefinite program. Moreover, for special matrix classes (tridiagonal, backward tridiagonal and cyclic Hankel matrices) we show that the above form is sos. Finally, we conjecture sos representability for Toeplitz matrices.

MSC:
90C22 Semidefinite programming
15A45 Miscellaneous inequalities involving matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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