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Suppose I have a function $\phi(M):=M^n$ where $M\in M_n(R)$

Does it make any sense to talk about the derivative of this function? What would it mean if it does make sense? I am also wondering what the derivative (if it exists and is meaningful) would be. (Perhaps $nM^{n-1}$?)

Thanks.

  • 1
    Look up [Gâteaux](https://en.wikipedia.org/wiki/G%C3%A2teaux_derivative) and [Fréchet](https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative) derivatives.2011-11-22
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    I'd just like to say that this is a great question - keep on thinking about how ideas you've learned in different mathematical contexts might interact!2011-11-22

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