合同变换

引入初等相似变换与初等合同变换，使化方阵为Jordan标准形的同时求得相似变换阵，化实对称阵为对角阵的同时求得合同变换阵。

Introducing so called elementary similar transformation and elementary congruent transformation , we can obtain the corresponding transformation matrices when getting the matrices of the standard form of an quadratic form and Jordan standard form of a matrix .

相似变换阵与合同变换阵的初等变换求法

Calculating the Matrix of Similar Transformation and Congruent Transformation by Elementary Transformation

通过合同变换，n阶实对称矩阵的正定性完全可以由n-1阶实对称矩阵的正定性确定，从而得到一个判定正定矩阵的充分必要条件，用它可以降阶判别矩阵的正定性。

The positive definition of n order real symmetric matrix can be determined by n 1 order real symmetric matrix with congruent transformation . And one necessary and sufficient condition of a positive definite matrix is proved , it can judge positive definite matrix with reducing to a lower order .

利用合同变换求循环矩阵的逆及其行列式的值

Finding the inverse of cyclic matrices and the values of their determinants

关于合同变换矩阵的一般形式

General Form of the Change of Matrix in Congruent Matrices

分块矩阵的相似变换和合同变换

The Similar Transformation and Congruent Transformation of Block Matrix

用矩阵的合同变换法求标准正交基

On a Method of Determining a Normal Orthogonal Basis

本文给出了二次曲线的几种化简方法，其中对合同变换法化简中心二次曲作了一点探讨

This passage offers several methods of simplifying the conic Among them is the Method of Congruent transformation

给出了二次型化标准形的两种方法&合同变换法和正交变换法。

Two methods of transforming quadratic form into standard form are introduced in this article + & method of congruent transformation and method of orthogonal transformation .

本文介绍了广义初等矩阵与广义初等变换的概念以及它们在求逆矩阵、行列式计算、求秩和在矩阵的合同变换方面的应用。

This paper introduces the concepts of generalized elementary matrix and generalized elementary transformation as well as the applications of calculating matrix inversion , determinant , rank and contract transformation .

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。

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 .

笔者利用合同变换，给出了计算这类矩阵之逆及其行列式值的简捷方法。

The author proposes , by way of contract transformation , a procedure to give a convenient and simplified representation of the inverses of cyclic matrices and a procedure to calculate the values of their determinants .