This
paper presents a new type of circulant matrices. We call it the first and the
last difference r-circulant matrix (FLDcircr matrix). We can
verify that the linear operation, the matrix product and the inverse matrix of
this type of matrices are still FLDcircr matrices. By constructing the basic FLDcircr matrix, we give the discriminance for FLDcircr matrices and the fast algorithm of the inverse and generalized inverse of the FLDcircr matrices.
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