       Re: Strange Det function behavior.

• To: mathgroup at smc.vnet.net
• Subject: [mg65463] Re: Strange Det function behavior.
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Mon, 3 Apr 2006 06:59:28 -0400 (EDT)
• Organization: Universitaet Hannover
• References: <e0o513\$1to\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Alexander schrieb:
> Dear MathGroup!
>
> Suppose we have defined the following function:
>
> f[x_Integer] := Det[ Table[ Random[]*t + i/j, {i, x}, {j, x} ] ];
>
> Now try to make a table for different values of argument (matrix
> dimension):
>
> Table[f[i], {i, 12}] // TableForm
>
> It takes a considerable time on my Celeron 1700 with Mathematica 5.2
> under WinXP to make such a table.
>
> Once we made this table we see very strange bihavior, all results
> before x=12 dimension are polynoms,
> but starting from x=12 result become very big and very
> strange, and in fact it's not even a polynom.
>
> I spend several hours try to understand why system acts so strange, and
> finally came to idea that the answer is in numbers representation and
> inner
> system algorithms used to evaluate Det function.
>
> It would be very interesting to see explanations of this result.
>

Perhaps the determinant is calculated using some transformations to
standard triangular form. The determainant then is a product of
determinant of matrices some of which are given in inverse form. So in
effect you get the determinant as a rational expression in the variable
"t". To proceed further you have to invert a matrix or to find the
common factors in the polynomials.

--

Roland Franzius

```

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