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From: <HIDDEN>
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Subject: Re: DETERMINANT OF 20 BY 20 MATRIX - higher precision for eigenvectors
Date: Thu, 14 Apr 2011 03:57:59 -0700
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On 4/14/2011 3:02 AM, Leo Kay wrote:

>
> Anyways, can anyone tell me why finding the determininant of a 20 y 20 symbolic matrix  fails?

May be becuase there is not enough RAM to hold the result?

Running this in Mathematica shows the size of the generated symbolic expression

matrixSize = 6
A=Table[Sin[n m x],{n,matrixSize},{m,matrixSize}];
Det[A]

For matrixSize = 5, number of individual symbolic expressions 1,807  (10^3)
For matrixSize = 6, number of individual symbolic expressions 11,358 (10^4)
For matrixSize = 7, number of individual symbolic expressions 83,065 (10^5)
For matrixSize = 8, number of individual symbolic expressions 666,005 (10^6)
For matrixSize = 9, number of individual symbolic expressions 6,080,591 (10^7)

You see that it is a factor of 2 larger each time.

So, for 20 by 20 symbolic matrix, with very simple symbolic entries,
one will get about 10^18 entries.

Assuming each symbolic expression requires say 100 characters to store,
then this requires 10^20 bytes, or about

100,000,000,000,000,000,000   bytes