Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics. Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices. The even-parity symmetries impose strict constraints on the scattering coefficients: the time-reversal (C and K) symmetries protect the symmetric transmission or reflection; the pseudo-Hermiticity (Q symmetry) or the inversion (P) symmetry protects the symmetric transmission and reflection. For the inversion-combined time-reversal symmetries, the symmetric features on the transmission and reflection interchange. The odd-parity symmetries including the particle-hole symmetry, chiral symmetry, and sublattice symmetry cannot ensure the scattering to be symmetric. These guiding principles are valid for both Hermitian and non-Hermitian linear systems. Our findings provide fundamental insights into symmetry and scattering ranging from condensed matter physics to quantum physics and optics.

对称性在物理学中起着基础作用，在非厄米物理学中对称性变化的本质。这里通过使用对随机矩阵进行分类的离散对称性来研究非厄米线性系统中的对称保护散射。偶校验对称性对散射系数施加了严格的约束：时间反转（C和K）对称性保护对称传输或反射；伪 Hermitity ( Q对称性) 或反演 ( P) 对称性保护对称传输和反射。对于反演组合的时间反演对称性，传输和反射上的对称特征互换。包括粒子-空穴对称、手征对称和亚晶格对称在内的奇宇称对称不能保证散射是对称的。这些指导原则对 Hermitian 和非 Hermitian 线性系统都有效。我们的研究结果为从凝聚态物理到量子物理和光学的对称性和散射提供了基本的见解。