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.

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

Both congruent and similarity of matrix are equivalence relations.

矩阵的合同关系、相似关系都是等价关系。

The Similar Transformation and Congruent Transformation of Block Matrix

分块矩阵的相似变换和合同变换

By means of congruent transformation in matrix, the method of transforming real quadratic form into standard form and the method of normal orthogonal basis are given in this paper.

借助矩阵的合同变换法，给出了化实二次型为标准形的方法、求标准正交基的方法，并给出了正定二次型判定定理的新证明。

A new concept of congruent matrix is introduced in the paper and its equivalent transformations are discussed.

本文引进了同馀矩阵的新概念，并讨论了它的等价变换。

Butterfly Mechanism consists of two congruent equilateral triangles.

蝶形单元是由两个全等的三角形组成。

Exploring the Best Method of Testifying the Congruent Right Triangles

探索直角三角形全等的最佳途径

Secondly, two new methods implemented easily about improvement with velocity compensation on the average time method are brought out, one is using Doppler velocity to compensate relative velocity, the other is using the estimated target speed in approximate congruent triangles.

提出两种易于实现的、对时间平均进行速度补偿的方法：一是利用多卜勒测速结果进行径向速度补偿；二是在近似三角形内，利用目标的估计速度进行补偿。

In the matching process the parameters of rotation and displacement were obtained by two congruent triangles, then the point-pairs matching would be performed on the transformed sets.

比对过程中首先根据两个集合中的全等三角形求出它们的旋转和平移参数，然后对根据参数进行转换后的特征集合进行点模式匹配。

Determination of Congruent Melting Constituent of Li_2B_4O_7 Crystal Using Thermal Analysis Method

用热分析法测定Li2B4O7单晶的一致熔融组成

The α phase is a congruent melting compound, its congruent melting point is 1 190 ℃. The β phase is an incongruent melting compound, its incongruent melting point ( peritectic temperature) is 1 100 ℃.

α相是熔点为1190℃的同成分熔融化合物，β相是转熔温度为1100℃的异成分熔融化合物。

The anomalous violet-shift of absorption edge of linbo_3 crystals of the solid-liquid congruent point composition

固液同成分点组分的LiNbO3晶体吸收边的异常紫移

Study of the ultraviolet absorption edge of LiNbO_3 crystal solid-liquid congruent point composition

固液同成分点组分LiNbO3紫外吸收边研究

The congruent point range and line pencils between two projective planes

两射影平面场的合同点列与线束

After congruence of lines changes into vector bundles, its correctness is proved, and theorem of Backlund is proved by using sections of bundles. A condition of iteration is given for seeking minimal area of a curved surface with fixed boundary curve.

将线汇转化成向量丛后从理论上证明了这种转化的正确性，利用向量丛的截面理论证明了Backlund定理并给出一种固定边界而求面积最小的曲面的迭代条件。

The paper presented the definition and properties of n-th completely linear subgroup on modulus of congruence class ring, and calculated the formula of factorial.

文中给出了模m的同余类环上的n阶完全线性子群的定义及性质，利用子群进行分类，通过陪集的计数定理，给出了其阶的计算公式。

Properties of n-th completely linear subgroup on modulus of congruence class ring

模m同余类环生成的n阶完全线性子群的阶的计算

Tensor Product of Normal Bands and Minimum Normal Band Congruence

正规带的张量积与极小正规带同余

In this paper, based on the relation between normal subgroup and congruence, another depiction of normal series power semigroup is given from the angles of congruence by the method of analogy.

首先在正规子群与同余的关系的基础上，采用类比的方法，从同余的角度给出了群的正规列幂半群的另一种刻画。