Re: true limit of mathematica ? Help me !!!

• To: mathgroup at smc.vnet.net
• Subject: [mg60249] Re: true limit of mathematica ? Help me !!!
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 8 Sep 2005 04:53:44 -0400 (EDT)
• Organization: The University of Western Australia
• References: <dfm7o5\$h9q\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <dfm7o5\$h9q\$1 at smc.vnet.net>,
LumisROB <lumisrob_NOGOOD_ at yahoo.com> wrote:

> During this calculation:
>
> m= Table[(i-j)+3.*j^-4 +50*I,{I,1,10000},{j,1,10000}];
> Det[m]
>
> the kernel has jammed and the following message has been visualized
> No more memory available.
> Mathematica kernel has shut down.

And you are suprised by this? You are attempting to construct,
explicitly, a 10^5 x 10^5 non-sparse matrix, which has 10^10 entries,
and then compute its Det.

> Is it possible to overcome this obstacle?

Yes. Two observations:

[1] Your first iterator is I, which is Sqrt[-1]. You mean i.

[2] Consider

mat[n_] := Table[(i-j) + 3 j^-4 + 50*I,{i,n},{j,n}]

which is an exact (I've replaced 3. by 3) n x n representation of your
matrix. Computing the Det for n = 1, 2, ..., 10, you will observe that
the Det[mat[n]] is 0 for n >= 3. Why?

Clearly the matrix must be singular. It is easy to show that the first 3
rows are not independent. In fact

{497/1647, -2144/1647, 1, 0, 0, ..., 0, 0, 0}

(where there are n - 3 zeros after the 1) is a member of the null space
of mat[n]. Hence the answer you are after is 0.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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