标题： 通过矩阵柯西-施瓦茨不等式的李猜想的新的证明 显示英文标题

标题： A new proof of Lee's conjecture on the Frobenius norm via the matrix Cauchy-Schwarz inequality

摘要： 2010年，Eun-Young Lee猜想，如果$A,B$是两个$n\times n$复矩阵，$\left|A\right|, \left|B\right|$分别是$A, B$的绝对值，那么\[ \|A+B\|_F\le \sqrt{\dfrac{1+\sqrt{2}}{2}}\|\left|A\right|+\left|B\right|\|_F, \]，其中 $\|\cdot\|_F$是矩阵的Frobenius范数。 该猜想通过研究由Frobenius内积引起的两个矩阵之间的角度不等式，由Lin和Zhang [J. Math. Anal. Appl. 516 (2022) 126542]证明。 在本文中，我们提供了一个新的证明，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 has been 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.