狭义相对论中的基变换与Gram-Schmidt正交化
Change of basis and Gram-Schmidt orthonormalization in special relativity
摘要：
虽然显式基在欧几里得空间的研究中很常见，但它通常隐含在惯性相对论系统的研究中。在狭义相对论系统的研究中，包含基础有一些概念上的优势。一个Minkowski度量意味着一个非标准正交基，为了处理这种复杂性，引入了互反基和向量对偶的概念。它示出了倒易的基础是如何与上下索引坐标提取，度量张量，基础的变化，在非正交基的投影，最后的Gram-Schmidt程序。它将表明，洛伦兹变换可以被看作是基础操作的变化。在一个空间维度的洛伦兹助推将使用Gram-Schmidt正交归一化算法导出，它将显示如何其他洛伦兹变换可以使用Gram-Schmidt程序导出。
英文摘要：
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic systems. A Minkowski metric implies a non-orthonormal basis, and to deal with this complexity the concepts of reciprocal basis and the vector dual are introduced. It is shown how the reciprocal basis is related to upper and lower index coordinate extraction, the metric tensor, change of basis, projections in non-orthonormal bases, and finally the Gram-Schmidt procedure. It will be shown that Lorentz transformations can be viewed as change of basis operations. The Lorentz boost in one spatial dimension will be derived using the Gram-Schmidt orthonormalization algorithm, and it will be shown how other Lorentz transformations can be derived using the Gram-Schmidt procedure.
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