Through the matrix rank method,this note prove that the following results:[A,B]+=[αA+βB+]βAAαBB.

The generalized reflection-transmission coefficient matrix method for synthetic seismograms;

For arbitrarily spatial elastic curved rod elements with circular cross-section, a set of displacement functions fully reflecting the rigid body modes is derived using the classical elasticity theory and mathematic theories of the differential geometry and matrix methods.

3-D rigid--plastic FEM and matrix method are adopted to calculate plastic deformation of strip and elasticdeformation of rolls respectively.

Considering the mechanical and electrical boundary conditions of AlN/GaN structures,determinantal equation which is used to solve the phase velocity of surface acoustic wave(SAW) is given from the basic principle of matrix methods.

The complex beam parameters in spherical resonators with an aperture is analyzed by matrix methods.

In this thesis, the propagating properties of surface acoustic wave (SAW) in AlN/GaN structures were researched by the Adler matrix methods.

By means of the rank of matrix, line outspreading, it gives some conditions in which a matrix can decompose to two Kronecker products of matrix.

In this note,we describe the equivalent propositions on the rank of matrix by determinants,equivalent of matrix,system of linear equations,linear space,linear mapping and so on.

Necessary and sufficient conditions for the Frobenius inequality of rank of matrix to be equality are dicussed in this paper,and the characterization of rank of a class of matrix is characterized.

The way to determine the reflexive g-inverse of full rank matrix A was discussed.

Secondly,the randomly generating of full rank matrix and per-muta.

This paper discusses the way about how to get the reflexive general inverse matrix of a full rank matrix A, and generalize this way, gives the general way for not full rank matrix.

This paper summarizes the applications of elementary transformation of matrix in solving the rank of a matrix or a set of vectors,calculating inverse matrix or system of linear equations,and solving the system of linear equations and the greatest common divisor of polynomials with examples,furthermore,it introduces the thought and application of generalized elementary transformation.