Abstract
For fixed real or complex matrices A and B, the well-known von Neumann trace inequality identifies the maximum of |tr( UAVB)z.sfnc;, as U and V range over the unitary group, the maximum being a bilinear expression in the singular values of A and 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.
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