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Matrix Series


Greetings,

Consider the familiar series expansion

   Log[x] = (x-1)  -1/2*(x-1)^2 + 1/3*(x-1)^3 - 1/4*(x-1)^4 + ....

I am interested in having Mathematica (v4.1) numerically evaluate an m-term
matrix counterpart to this expansion, e.g.,

    Q[X_,m_] := (X-I) - 1/2*(X-I)^2 + 1/3*(X-I)^3 - 1/4*(X-I)^4 + ....
1/m*(X-I)^m


where X is an nxn real matrix and I is the nxn identity matrix, and m is
some positive integer.

I've been struggling with the built-in Series[] function, but it is not
obvious to me how to generalize it to handle matrix arguements. My other
alternative is to just to use the 'MatrixPower' function and build-up
the (alternating-sign) sequence of series coefficients in a Table[]
command, as I only need the numerical result. But my curiosity has been
piqued and I was wondering if there is someother way to do this.

Help!!

Thanks,

Mark


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