Abstract: This paper discusses the relation between congruent matrices and similar matrices in linear algebra and their use in geometry
本文讨论了线性代数中合同与相似之间的关系及在几何中的应用
General Form of the Change of Matrix in Congruent Matrices
关于合同变换矩阵的一般形式
The relationship within non-degenerate linear substitutions which changes quadratic forms into gauge forms over real number field or complex number field and introduction the result into congruent matrices are discussed in this paper.
本文探讨了把实数域或复数域上的二次型化为规范形所采用的非退化线性替换之间的关系,并引入到矩阵的合同关系中。
Some Special Matrices Congruent with Diagonal Matrices
几类特殊矩阵与对角矩阵的合同
In this paper we will discuss symmetric bilinear forms and quadratic forms over valuation rings, and establish the congruent standard forms of symmetric matrices over valuation rings.
本文讨论赋值环上的对称线性型、二次型和对称矩阵的合同标准形。
For given congruent real symmetric matrices A and B of n-th-order, the author gives here the general form of their complex congruent transformation.
对给定的合同的实对称n阶阵A和B,给出其复合同变换的一般表示形式。
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