Sum of squares representation for the Böttcher-Wenzel biquadratic form
arXiv:1207.6372
Abstract
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 semide finite 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.