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