Abstract

We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail, and also discuss the extension to three-dimensional vector spaces.

中文翻译：

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保长方向和一些丢番图方程

摘要

我们研究在线性映射下矢量范数得以保留的方向。特别是，我们发现矩阵的族，这些方向由整数矢量确定。我们将详细考虑二维情况，并讨论对三维向量空间的扩展。