Rank Equalities for Moore-penrose Inverse and Drazin Inverse over Quaternion
نویسندگان
چکیده
In this paper, we consider the ranks of four real matrices Gi(i = 0, 1, 2, 3) in M†, where M = M0 +M1i+M2j+M3k is an arbitrary quaternion matrix, and M† = G0 + G1i + G2j + G3k is the Moore-Penrose inverse of M . Similarly, the ranks of four real matrices in Drazin inverse of a quaternion matrix are also presented. As applications, the necessary and sufficient conditions for M† is pure real or pure imaginary Moore-Penrose inverse and N is pure real or pure imaginary Drazin inverse are presented, respectively.
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The perturbation of the Drazin inverse and oblique projection
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