从矩阵次对角线的角度考察矩阵的性质

Examining the Properties of Matrices in Terms of Their Subdiagonals

摘要: 本论文不同于以往研究者大多数从矩阵主对角线方向去讨论矩阵的性质，而是从矩阵次对角线角度考察矩阵的性质，提出次转置、次对称、次单位、次正交、次可逆矩阵的概念，得到了大体有趣的新结果。对于开阔读者的视野，以及进一步研究矩阵性质有一定的启发作用，相信在一些领域会有一定的应用。

Abstract: This paper is different from the previous researchers who mostly discuss the properties of matrix from the direction of the main diagonal of matrix, but investigate the properties of matrix from the perspective of sub diagonal of matrix, put forward the concepts of sub transpose, sub symmetry, sub unit, sub orthogonal and sub reversible matrix, and obtained generally interesting new results. It has a certain enlightening effect on broadening readers’ horizons and further studying matrix properties. I believe it will be applied in some fields.