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Any suggestions at to what matrix $B$ is such that$\|X[(I+YX)^{-1}-I]-BY\|=O(\|Y^a\|)$ where $a>1$ and $X,Y,B$ are all square matrices of the same size and $I$ is the identity matrix and $\|\cdot\|$ is a norm?

Also, to be clear $O(\cdot)$ is the big-$O$ notation .

Thank you.

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What does big-O mean for matrix-valued functions? –  user7530 Nov 23 '11 at 16:15

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