For fixed real or complex matrices A and B, the well known von Neumann trace inequality identifies the maximum of ⎸tr(U AV B) ⎸, as U and V range over the unitary group, the maximum being a bilinear expression in the singular values of A y B. This paper establishes the analogue of this inequality for real matrices A and B when U and V range over the proper (real) orthogonal group. The maximum is again a bilinear expression in the singular values but there is a subtracted term when A and B have determinants of opposite sign.
@article{1574,
title = {A trace inequality with a subtracted term},
journal = {CUBO, A Mathematical Journal},
year = {1992},
language = {en},
url = {http://dml.mathdoc.fr/item/1574}
}
Miranda, H.; Thompson, Robert C. A trace inequality with a subtracted term. CUBO, A Mathematical Journal, (1992), 7 p. http://gdmltest.u-ga.fr/item/1574/