Re: Matrix Inverse Issue

• To: mathgroup at smc.vnet.net
• Subject: [mg80604] Re: Matrix Inverse Issue
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sun, 26 Aug 2007 23:12:45 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <far922\$3t8\$1@smc.vnet.net>

```Brian Gladman wrote:
> I am having a problem with the matrix inverse for the following matrix in
> Mathematica 6:
>
> A = Table[If[j == i, 1 - i/10, If[j == i + 1, i/10, 0]], {i, 9}, {j, 9}]
>
> {{9/10, 1/10, 0, 0, 0, 0, 0, 0, 0}, {0, 4/5, 1/5, 0, 0, 0, 0, 0,
>   0}, {0, 0, 7/10, 3/10, 0, 0, 0, 0, 0}, {0, 0, 0, 3/5, 2/5, 0, 0, 0,
>   0}, {0, 0, 0, 0, 1/2, 1/2, 0, 0, 0}, {0, 0, 0, 0, 0, 2/5, 3/5, 0,
>   0}, {0, 0, 0, 0, 0, 0, 3/10, 7/10, 0}, {0, 0, 0, 0, 0, 0, 0, 1/5, 4/
>   5}, {0, 0, 0, 0, 0, 0, 0, 0, 1/10}}
>
> A Inverse[A]
>
> {{1, -1/72, 0, 0, 0, 0, 0, 0, 0}, {0, 1, -1/14, 0, 0, 0, 0, 0, 0}, {0,
>    0, 1, -3/14, 0, 0, 0, 0, 0}, {0, 0, 0, 1, -8/15, 0, 0, 0, 0}, {0,
>   0, 0, 0, 1, -5/4, 0, 0, 0}, {0, 0, 0, 0, 0, 1, -3, 0, 0}, {0, 0, 0,
>   0, 0, 0, 1, -49/6, 0}, {0, 0, 0, 0, 0, 0, 0, 1, -32}, {0, 0, 0, 0,
>   0, 0, 0, 0, 1}}
>
> I expected the identity matrix here but I get extra terms.
>
> Am I doing something wrong?

Yes. Use the dot product (Dot or .) for matrix multiplication, otherwise
you get a term by term multiplication.

In[1]:= A =
Table[If[j == i, 1 - i/10, If[j == i + 1, i/10, 0]], {i, 9}, {j,
9}];

In[2]:= A.Inverse[A] == IdentityMatrix[Length[A]]

Out[2]= True

--
Jean-Marc

```

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