| Circulate 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 characters and matrix inversion technique of several special circulates matrices and several special block circulate matrices basing on a flood of references.Detail as follows:Chapter one It gives the relevant background knowledge, mainly about the study of circulate matrices at home and abroad, the basic concepts, characteristics of circulate matrices, and the basic computing instruments which have been frequently used in matrix theory and matrix calculations.Chapter two It studies the characters of skew-symmetric and skew-circulate matrix. Based on the special characters of this kind of matrices and using the Fourier matrix and Vandermonde matrix, we analyze particular laws and special characters of skew-symmetric and skew-circulate matrices'eigenvalues and eigenvectors. At the last of this chapter, we get some matrix inversion techniques of skew-symmetric and skew-circulate matrix.Chapter three We get the expression of symmetric r-circular matrices through the relation of symmetric r-circular matrices, r-circular matrices and symmetric skew-circulate matrix. We further discuss basic characters, necessary and sufficient condition of reversibility of this kind of matrices, and get the matrix inversion technique and necessary and sufficient condition of judging a matrix is a symmetric r-circular matrix or not.Chapter four We extend some characters of circular and skew-symmetric matrix and symmetric r-circular matrices to block circular and skew-symmetric matrix and block symmetric r-circular matrices. This study further enriches the content of block circular matrices.
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