3. (Bhatia-Davis) 设 $A,B\in M_n$ 为酉矩阵, 则 $$\bex \rd(\sigma(A),\sigma(B))\leq \sen{A-B}_\infty. \eex$$

证明: [见 R. Bhatia, C. Davis, A bound for the spectral variation of a unitary operator, Linear and Multilinear Algebra, 15 (1984), 71--76.]

[詹兴致矩阵论习题参考解答]习题5.3