块循环阵的特征值与非异性

EIGENVALUES AND NONSINGULARITY OF A BLOCK CYCLIC MATRIX

给出在矩阵论和物理学等应用学科上极为需要的块循环阵Ａ￣［１］和复对出循环阵的特征值的具体形状，并给出判断Ａ非异的简便方法。推广了￣［２］的结果。

It is necessary to find the concrete manner of eigenvalues of a block cyclic matriX in appliedmatrix and physics. This paper gives the concrete expressions of all the eigenvalues of an mn × mn blockcyclic matrix and n×n complex symmetric cyclic matrix .This paper also provides a discrimination on nonsingulatiey of block cyclic matrices.