Block Independence in Various Generalized Inverses of Partitioned Quaternion Matrices

Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and...
Ausführliche Beschreibung

Abstract In this paper, we derive some necessary and sufficient conditions for two, three and four quaternion matrices to be block independent in the least squares inverse, the minimum norm inverse and the {1,3,4}-inverse, respectively. Moreover, it is shown that, quite surprisingly, two, three and four ordered quaternion matrices are block independent in the {1,3,4}-inverse if and only if they are block independent in the Moore–Penrose inverse, which at first glance looks to be a weaker condition than the later. Ausführliche Beschreibung