vectorial ODE in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg126768] vectorial ODE in mathematica*From*: volatility quant <volatility.quant at gmail.com>*Date*: Wed, 6 Jun 2012 04:52:33 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

I want to solve the following equation in mathematica : DSolve[{X'[t] == A.X[t], X[0] == ( {{0},{0}} )}, X[t], t] It is a system of 2 ODEs coupled by the matrix A, that I don't want to put in the form {{a,b},{c,d}} in order to have the output as a function of matrix exponential. Mathematica understands that but gives a solution strangely expresed as : {{X[t] -> InverseFunction[Dot, 2, 2][A, E^(t A.1) InverseFunction[InverseFunction[Dot, 2, 2], 2, 2][A, 0]]}} Where it indeed uses a matrix exponential, but also relies on a strange notation InverseFunction [...] My question is how to get rid of this InverseFunction notation to have a more readable expression. Do I for example have a manner to postulate that A is a (2,2) matrix, invertible, with inverse B? Thanks a lot for help