IEEE Transactions on Automatic Control, Vol.42, No.4, 578-581, 1997
Tight Bounds for the Trace of a Matrix Product
We propose a family of new upper and lower bounds for the trace of the matrix product AB when A or B is symmetric. Those bounds depend on a scalar parameter, and both converge monotonically to tr (AB) when this parameter vanishes, thus providing arbitrary close approximations. Even large values of the parameter yield very good bounds.