We investigate the real space H of Hermitian matrices in $M_n(\mathbb{C})$ with respect to norms on $\mathbb{C}^n$ . For absolute norms, the general form of Hermitian matrices was essentially established by Schneider and Turner [Schneider and Turner, Linear and Multilinear Algebra (1973), 9–31]. Here, we offer a much shorter proof. For non-absolute norms, we begin an investigation of H by means of a series of examples, with particular reference to dimension and commutativity.

中文翻译：

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具有算子范数的矩阵代数中的厄米特

我们调查真实的空间HHermitian 矩阵$M_n(\mathbb{C})$关于规范$\mathbb{C}^n$. 对于绝对范数，Hermitian 矩阵的一般形式本质上是由 Schneider 和 Turner [Schneider and Turner,线性和多线性代数（1973），9-31]。在这里，我们提供了一个更短的证明。对于非绝对规范，我们开始调查H通过一系列例子，特别是维度和交换性。