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]

```

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