关于块对角因子循环矩阵的对角化与可逆性

Diagonalization and invertibility of block diagonal factor circulant matrices

提出了复数域上的块对角因子循环矩阵并讨论了它的对角化、特征值、特征向量和行列式,同时给出了仅用这类特殊矩阵第一行的元素和基本对角因子循环矩阵的元素就可断定这类特殊矩阵可逆性的3个充分条件.

A block diagonal factor circulant matrix over the complex field is introduced. The diagonalization, eigenvalue, eigenvector and determinant of such matrices are discussed. Only by the relation between the entries of the first row of such matrices and the entries of basic diagonal factor circulant matrix do we give three sufficient conditions for determining its invertibility.