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MathGroup Archive 2006

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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.
> 
> Thanks for your answers!

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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