Inverse of symbolic matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg88326] Inverse of symbolic matrix*From*: Hugh Goyder <h.g.d.goyder at cranfield.ac.uk>*Date*: Fri, 2 May 2008 03:40:54 -0400 (EDT)

The expressions a and b below seem reasonable. However when I assemble them into a matrix and take the inverse I get the message Inverse::"sing" :Matrix...is singular. However the determinant seems fine. If I rationalize the matrix and then take its inverse then everything seems fine and I can almost get the unit matrix by multiplying back onto the original matrix. Is there a problem with approximate numbers in symbolic matrices? Is this a bug? Is Rationalize the best method for working around this problem? Thanks Hugh Goyder a = -((4.739*^-6 - 0.0008*I)/((0.0122 + 1.544*I) + s)) - (4.7395*^-6 + 0.00088*I)/ ((0.0122 - 1.544*I) + s); b = -((0.000015 - 0.00022*I)/((0.0122 + 1.544*I) + s)) - (0.000015 + 0.000226*I)/ ((0.0122 - 1.544*I) + s); mat = {{a, 0}, {0, b}}; Inverse[mat] Det[mat] matr = Rationalize[mat, 0]; inv = Inverse[matr] Rationalize[Factor[Together[mat . inv]], 1.*^-8]