论文标题
无维矩阵空间
Dimension-Free Matrix Spaces
论文作者
论文摘要
根据各种类型的矩阵半张量产物，提出了相应的矩阵等效性。然后，相应的矢量空间结构作为等价下的商空间获得，称为无维矩阵空间（DFESS）。研究某些结构和特性。最终，将通用线性代数的谎言支架结构扩展到DFMS，使其为代数为代数，称为无尺寸的一般线性代数（DFGLA）。 dfglas具有无限尺寸的事实，它们具有有限维度的大多数代数，在论文中研究了whicl。
Based on various types of semi-tensor products of matrices, the corresponding equivalences of matrices are proposed. Then the corresponding vector space structures are obtained as the quotient spaces under equivalences, which are called the dimension-free Matrix spaces (DFESs). Certain structures and properties are investigated. Finaly, the Lie bracket structure of general linear algebra is extended to DfMSs to make them Lie algebras, called dimension-free general linear algebra (DFGLA). Inspire of the fact that the DFGLAs are of infinite dimension, they have most properties of finite dimensional Lie algebras, whicl are studied in the paper.
