Eigenvalues of a kind of circulant matrices and its application on subdivision;

VLSI decoding design of low-density parity-check codes based on circulant matrices

Making use of some relations between discrete Fourier transformation and convolution, I give a sufficiency and necessary condition which estimates that a matrix is a circulant matrix, and give concretely an accounting formula of m-orders circulant matrices.

An algorithm for computing the inverse of two kind circulant matrix;

On the properties and generalized inverse of (-1)-circulant matrix

Based on the special charicteristics of circulant matrix, a new formula of inversion for a type of specific matrix is proved in this paper.

Four theorems are presented and proved for eigenvalues and eigenvectors of circular matrix including symmetrical circular matrix, which forms the uniform mathematical principle of phase-sequence transformation for 3-phase and high phase order AC power networks.

Circular matrix may be diagonalized while diagonalized matrix is equal to similar circular matrix.

The generalization of a theorem for circular matrix is given by using generalized Vandermonde matrix,and several properties of generalized circular matrix are obtained.

Maximal general Armendariz subrings of matrix rings;

Using properties of idempotents,we show several necessary and sufficient conditions for the invertibility of the difference of two idempotents, and exhibit some applications to matrix rings.

And the results are extended to n×n matrix rings.