Ela Representations for the Drazin Inverse of Block Cyclic Matrices
نویسنده
چکیده
REPRESENTATIONS FOR THE DRAZIN INVERSE OF BLOCK CYCLIC MATRICES M. CATRAL AND P. VAN DEN DRIESSCHE Abstract. A formula for the Drazin inverse of a block k-cyclic (k ≥ 2) matrix A with nonzeros only in blocks Ai,i+1, for i = 1, . . . , k (mod k) is presented in terms of the Drazin inverse of a smaller order product of the nonzero blocks of A, namely Bi = Ai,i+1 · · ·Ai−1,i for some i. Bounds on the index of A in terms of the minimum and maximum indices of these Bi are derived. Illustrative examples and special cases are given.
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