Study On Algorithms And Properties Of Several Special Circulate Matrices

Circulant matrices are an important component of the matrix theory. Because they have a lot of good properties and structures ,and are extensively adopted in the field of modern science and technology, circulate matrices have become one of the most important and active research fields of applied mathematics increasingly. So the research of these will bring out a lot of meaningful results.In this paper, we study some algorithms and properties of several special circulant matrices and some properties of several special block circulant matrices basing on a flood of references. Detail as follows:Chapter one It gives the relevant background knowledge, mainly about the study of circulant matrices at home and abroad,the basic concepts,properties of circulant matrices,and the basic computing instruments which have been frequently used in matrix theory and matrix calculations,kronecker product and vandermonde matrix.Chapter two It studies the properties of companion circulant matrix. Based on the diagonalizable of this kind of matrices and using the lagrange theorem, it gives us a algorithm for computing the inverse matrix of companion circulant matrix,a algorithm for computing the product matrix of two companion circulant matrices and a algorithm for computing m-th root matrices of n order companion circulant matrix. The chapter gives examples respectively.Chapter three It studies the properties of anticircular antisymmetric matrix,and gives a algorithm for computing m-th root matrices of n order anticircular antisymmetric matrix and a algorithm for computing the product matrix of two anticircular antisymmetric matrices. Chapter four It gives the definitions of block companion circulant matrix, generalized block companion circulant matrix and level-2 companion circulant matrix,then their properties are studied.