Matrix Series

*To*: mathgroup at smc.vnet.net*Subject*: [mg32138] Matrix Series*From*: "Coleman, Mark" <mark.coleman at dri-wefa.com>*Date*: Sat, 29 Dec 2001 00:47:00 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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