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Suppose we have

$$(A + I)^n$$

where $A$ is matrix and $I$ is an identity matrix. Does the binomial theorem apply?

I know the binomial theorem but not whether it is also applicable to matrices.

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2 Answers 2

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Sure. You could prove it the same way. It works because there is no difficulty about elements commuting in the case you have chosen. But it would not work for $(A+B)^n$

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Think about how binomial theorem is proved. You would quickly realize that the theorem can be proved by the same way for $(A+B)^n$ if $A$ and $B$ commute.

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  • $\begingroup$ What if matrices do not commute? In particular I have to compute the trace of $L=D-A$ to the power of $k$, like $Tr[L^k]$, but matrices do not commute. $\endgroup$
    – linello
    Aug 30, 2019 at 14:42

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