洛伦兹变换矩阵的对角化及其意义

Diagonalization of Lorentz transformation matrix and its significance

通过对角化过程,讨论洛伦兹变换矩阵特征矢量、特征值的意义.将洛伦兹变换矩阵对角化,即将一般惯性参考系变换到光锥坐标系.特征矢量是光锥坐标系坐标轴上的矢量.特征值对应参考系变换下,光锥坐标分量的缩放大小.本文可以帮助学生加深对洛伦兹变换及狭义相对论时空特性的理解.

The significance of eigenvectors and eigenvalues of Lorentz transformation matrix in the process of diagonalization are discussed.The procedure of diagonalizing Lorentz transformation matrix is to transform the general inertial frame of reference into the light-cone coordinate system.The eigenvectors are the vectors on the axis of light-cone coordinate system.The eigenvalues correspond to the scaling factor for the light-cone coordinate components under the reference frame transformation.This paper can help students to deepen their understanding of Lorentz transformation and the space-time characteristics of special relativity.