矩阵的几种标准形及其应用

矩阵的几种标准形及其应用

摘 要：矩阵的研究有极其丰富的内容．矩阵的标准形无论在理论上还是在应用上都有10分重要的地位．本文以矩阵的标准形为研究对象，以实例的方式，探讨了矩阵在等价变换，合同变换，相似变换下的标准形及其在矩阵的分解，矩阵的秩和矩阵的特征值等方面的应用．

关键词：等价变换；合同变换；相似变换；矩阵

Some Canonical Forms of the Matrix and Their Applications

Abstract: The research of matrices contains very abundant contents. The canonical form of the matrix has the very important position regardless on theories or applications. This paper regards the canonical form of the matrix as research object, probes into the canonical form of the matrix under the equivalent transformation, symmetric transformation, similarity transformation and its applications on decomposition of matrices, rank of matrices, eigenvalue of matrices and so on, by living example.

Keywords: equivalent transformation; symmetric transformation; similarity transformation; matrices