# Find an inverse matrix, regarding a parameter as real

I have the matrix

{{3, 2, 1}, {3, 1, 2}, {2, 3, -1},
{-(3/b), -(3/b^2) - 2/b, -(3/b^3) - 2/b^2 - 1/b},
{-(3/b), -(3/b^2) - 1/b, -(3/b^3) - 1/b^2 - 2/b},
{-(2/b), -(2/b^2) - 3/b, -(2/b^3) - 3/b^2 + 1/b}}


and I want to compute its inverse (or pseudoinverse).

The problem is that Mathematica solves this regarding b as a complex number. How do I change this to set b as real? I tried Assuming but that didn't work. Maybe I am writing it wrong. Any ideas? It should be fairly simple, but I am not really good at Mathematica and I couldn't find a solution elsewhere. I would be greatful for a general answer, not one specifically for this example; e.g., Pseudoinverse[a] /. Reals[b] -> ... (this didn't work).

Thanks

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Try ComplexExpand[PseudoInverse[mat]]. – b.gatessucks Nov 17 '12 at 15:16

Usually simplifying the result with appropriate assumptions gives desired result:

m={{3, 2, 1},
{3, 1, 2},
{2, 3, -1},
{-(3/b), -(3/b^2) - 2/b, -(3/b^3) - 2/b^2 - 1/b},
{-(3/b), -(3/b^2) - 1/b, -(3/b^3) - 1/b^2 - 2/b},
{-(2/b), -(2/b^2) - 3/b, -(2/b^3) - 3/b^2 + 1/b}};

Simplify[PseudoInverse[m], b \[Element] Reals]

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Yes thats true,it works just fine, thank you very much you have been very helpful! – Lazaros Moysis Nov 17 '12 at 15:22