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I need to work out the Integral $$\int \frac{1}{(x\mathbb{1}-A)^2}B\frac{1}{x\mathbb{1}-C}\ dx$$ Where $A,B,C$ are matrices which generally do not commute and $x$ is real. $\mathbb{1}$ denotes the identity matrix. I am ok with using matrix functions like $\log(x-A)$ defined by their taylor expansion.

The result in the commutative case is obvious, but I am not sure how to generalize to the non commuting case.

Hagadol
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  • By $x1$ do you mean $x^1 = x$? If not, then what? By the way, Hagadol is quite a moniker; yitgadol yitkaddash sh'meh rabbah! Chappy Chanukah and other Seasonal Greetings! Cheers! – Robert Lewis Dec 08 '14 at 18:01
  • @RobertLewis Thank you four your nice comment! I now added, the $\mathbb{1}$ is supposed to be the unity matrix. – Hagadol Dec 08 '14 at 18:10
  • You are more than welcome! By the way, most folks would use $I$ instead of $1$ for the identity matrix, just so you know. Baruch HaShem! – Robert Lewis Dec 08 '14 at 18:14

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