Abstract
Let A be an m × n complex matrix and let B, C be n × m complex matrices. The main purpose of this article is to derive several new properties of the (B, C)-core inverse. Also, we introduce and investigate the dual (B, C)-core inverse in the context of rectangular matrices. The connection between (dual) (B, C)-core inverses and other generalized inverses is given. Finally, the minimum norm solution and least square solution to the equation are expressed by using the (B, C)-core inverse.
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