Geometry of Matrices
Geometry of Matrices
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DOI：
10.2969/aspm/02410443
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Z. Wan
中科院分区：
文献类型：
--
作者：
Z. Wan
除环上的线性代数：除环上的矩阵，子空间的矩阵表示，线性方程组。第二部分仿射几何与射影几何：仿射空间与仿射群、射影空间与射影群、一维射影几何。第三部分矩形矩阵的几何：矩形矩阵的空间，基本定理在图论中的应用证明。第四部分交错矩阵的几何：交错矩阵的极大集空间。第5部分对称矩阵几何：对称矩阵空间基本定理I-III的证明。第六部分厄米特矩阵的几何：秩1的极大集基本定理的证明（n ≥ 3的情况）秩2的极大集（n=2）基本定理的证明（n=2的情况）及其他。
Part 1 Linear algebra over division rings: matrices over division rings matrix representations of subspaces systems of linear equations. Part 2 Affine geometry and projective geometry: affine spaces and affine groups projective spaces and projective groups one-dimensional projective geometry. Part 3 Geometry of rectangular matrices: the space of rectangular matrices proof of the fundamental theorem application to graph theory. Part 4 Geometry of alternate matrices: the space of alternate matrices maximal sets. Part 5 Geometry of symmetric matrices: the space of symmetric matrices proof of the fundamental theorem I-III. Part 6 Geometry of hermitian matrices: maximal sets of rank 1 proof of the fundamental theorem (the case n is greater than or equal to 3) the maximal set of rank 2 (n=2) proof of the fundamental theorem (the case n=2) and others.