Over a general field and for an arbitrary positive integer k, those triangular matrices whose kth power is diagonal are explicitly characterized. This is then used to characterize those complex matrices whose kth power is normal. This gives corresponding results for matrices whose kth power is Hermitian or real symmetric. Our results generalize and imply a recent result about eventually normal and eventually Hermitian matrices.

中文翻译：

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幂法线矩阵

在一般域上和对于任意正整数k，那些k次方是对角线的三角矩阵被明确地表征。然后将其用于表征那些k次方为正态的复数矩阵。对于第k次幂为 Hermitian 或实对称矩阵，这给出了相应的结果。我们的结果概括并暗示了关于最终正常和最终 Hermitian 矩阵的最新结果。