Research On The Matrix Stretching Operations

Matrix stretching operations are important tool that conduct matrix, particular on the matrix equation. In recent years, the research on matrix stretching operational problems has been mainly carried out in two directions about the matrix row stretching and column stretching, and some simple properties have been discussed. The matrix stretching operations are studied respectively from four aspects on this thesis.Firstly, the research status and related results of matrix stretching operations have been introduced.Secondly, this is a special research on the matrix stretching operations. First of all, through the analysis and research on the matrix row stretching and column stretching, the regularities of matrix stretching operations are found. On this basis, the representations of the matrix eight stretching definitions are given, and matrix stretching operations are extended. Next, properties of the correlative matrixes defined by matrix stretching operations are introduced, and the stretching relationship between them is studied. At last, based on the analysis of the relationship between matrix and vector, the matrix and block matrix, the matrix stretching operations are applied in the vector stretching operations and the block matrix stretching operations, and representations of the vector stretching operations and block matrix stretching operations are given.Thirdly, analyses on Hadamard product, Kronecker product and matrix product are carried out respectively. On this basis, the relationships of the Hadamard product and Kronecker product, as well as the Kronecker product are analysed, and the stretching relationships used two kinds of special operations are discovered.Finally, applications of matrix stretching operations are elaborated respectively on matrix equation and magic square matrix.