标题： Lee 关于弗罗贝尼乌斯范数的猜想的一个自然且简短的证明 显示英文标题

标题： A natural and short proof of Lee's conjecture on the Frobenius norm

摘要： 2010年，Eun-Young Lee猜想，如果$A,B$是两个$n\times n$复矩阵，而$\left|A\right|, \left|B\right|$分别是$A, B$的绝对值，则\[ \|A+B\|_F\le \sqrt{\dfrac{1+\sqrt{2}}{2}}\|\left|A\right|+\left|B\right|\|_F, \]其中$\|\cdot\|_F$是矩阵的Frobenius范数。 该猜想最初由Lin和Zhang[J. Math. Anal. Appl. 516 (2022) 126542]通过研究由Frobenius内积引起的两个矩阵之间的角度不等式来证明。 在本文中，我们提出了一个新证明，仅依赖于Cauchy-Schwarz不等式。 显示英文摘要

摘要： In 2010, Eun-Young Lee conjectured that if $A,B$ are two $n\times n$ complex matrices and $\left|A\right|, \left|B\right|$ are the absolute values of $A, B$, respectively, then \[ \|A+B\|_F\le \sqrt{\dfrac{1+\sqrt{2}}{2}}\|\left|A\right|+\left|B\right|\|_F, \] where $\|\cdot\|_F$ is the Frobenius norm of matrices. This conjecture was initially proven by Lin and Zhang [J. Math. Anal. Appl. 516 (2022) 126542] by studying inequalities for the angle between two matrices induced by the Frobenius inner product. In this paper, we present a new proof of the same result, relying solely on the Cauchy-Schwarz inequality.