Abstract
In this paper, we consider the ranks of four real matrices $G_{i}(i=0,1,2,3)$ in $M^{\dagger},$ where $M=M_{0}+M_{1}% i+M_{2}j+M_{3}k$ is an arbitrary quaternion matrix, and $M^{\dagger}% =G_{0}+G_{1}i+G_{2}j+G_{3}k$ 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 $M^{\dagger}$ is pure real or pure imaginary Moore-Penrose inverse and $N^{D}$ is pure real or pure imaginary Drazin inverse are presented, respectively.
Citation
Huasheng Zhang. "Rank equalities for Moore-Penrose inverse and Drazin inverse over quaternion." Ann. Funct. Anal. 3 (2) 115 - 127, 2012. https://doi.org/10.15352/afa/1399899936
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