矩阵与空间分解
Matrix and space decomposition
本文从投影矩阵的角度来分析空间的分解。首先，探讨了低维空间的投影矩阵的具体形式。然后，根据几何意义讨论了投影矩阵在矩阵的对角化下的应用，使得投影矩阵的对角化更加简便。最后，简单地探讨了投影矩阵的迹的相关性质及如何用其来定义空间的维数。
his paper analyzes space decomposition by using the projection matrix. Firstly, the specific forms of projection matrix in low-dimensional space are discussed. Then, based on the geometric meaning of projection matrix, this paper presents an application of projection matrix in diagonalization, simplifying the diagonalization of projection matrix. At last, related properties of the trace of projection matrix and an application in defining the dimension of space are discussed.
蒲丹、任庆刚、姚俊
数学
基础数学投影矩阵空间分解矩阵对角化矩阵的迹
Fundamental Mathematicsprojection matrixspace decompositiondiagonalization of matrixtrace of matrix
蒲丹,任庆刚,姚俊.矩阵与空间分解[EB/OL].(2016-09-05)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/201609-29.点此复制
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