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Adding matrices for use in NDSolve input


Hello,

I have the following problem. I'm trying to integrate a matrix equation of the form:

S'[t]=A.S[t]+B
S[t]=0 (n x m)

where A and B are symbolic matrices. B is of dimension n x m and I intend S[t] to also be of this dimension. However when I input this differential equation mathematica assumes S[t] is an n x 1 vector and replicates this vector match B for addition:

S'[t]={A.S[t],A.S[t],...,A.S[t]}+B

How can I specify my intended dimension of S[t] without makes variables for the individual elements of S[t]? I've tried playing around with hold to delay interpretation of the summation but prevents evaluation of A and B and I suspect the delay of summation will not help when NDSolve releases the hold. How can I get mathematica to interpret this equation in the way I intend?


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