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Inverting a matrix with symbolic bounds


I'd like to invert a matrix whose dimensions are specified only
symbolically, but I'm not sure how to represent it in Mathematica (or if
Mathematica can do it). The matrix is:

a    b    b^2    ...    b^k
b    a    b    ...        b^(k-1)
b^2    b    a    ...    b^(k-2)
..                                .
..                                .
..                                .
b^k    b^(k-1)    ...    a

I tried representing this matrix as a list, using symbols in Table[], but
Mathematica won't evaluate the bounds when they are symbolic. Is there a way
to do this?

Any ideas would be greatly appreciated!!!
Thanks.
Jon Davis
jondavis at uiuc.edu




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