DDVV和BW不等式的推广
Some generalizations of the DDVV and BW inequalities
摘要：
本文将已知的实（反）对称和复（反）埃尔米特矩阵的DDVV型不等式推广到任意实、复和四元数矩阵。受Erdens-Mordell不等式的启发，建立了Clifford系统或Clifford代数所张成的子空间中矩阵的DDVV型不等式.我们还将Böttcher-Wenzel不等式推广到四元数矩阵。
英文摘要：
In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erdős-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system or a Clifford algebra. We also generalize the Böttcher-Wenzel inequality to quaternionic matrices.
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