By introducing right column transformation, author discusses the problem ofsimplifying process that some special matrices are congruent with diagonal matrices, And givessome important conclusions.

According to the vector linear dependent principle,a basic idea to seek the maximal linearly independent vector group by elementary column transformation was formed.

In the paper we obtain a method to evaluate standard orthogonal basis by translating a basis in into orthogonal basis and uniting orthogonal basis, for only third row elementary transformation is used and validate the method is easy and convenient by giving some concrete examples.

Improvement on the elementary transformation method of QR decomposition of matrix;

Application of elementary transformation of matrix;

Finding bases for sum and intersection of subspaces in Pn using elementary transformations;

A method of seeking Moore-Penrose s generalized inverse metrix through elementary operation;

This paper presents an approach to find out the matrix eigenvalue and eigenvector of an eigenmatrix using elementary operations, which is an easier and quicker way to obtain the similarity diagonalization of a matrix.

In this paper, a practical solving method and an expression of general solution of a matrix equation AXB=CYD are given by using matrix techniques and elementary operations on matrix.