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MathGroup Archive 2001

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Re: Det[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg28840] Re: Det[]
  • From: Erich Mueller <emuelle1 at uiuc.edu>
  • Date: Tue, 15 May 2001 00:59:14 -0400 (EDT)
  • References: <9dlcge$o33@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You can do this one analytically without mathematica, however
mathematica is usefull for guessing the right form.  Try smaller
matrices with the same structure:

Ex. 
Det[{ {1,1,1},{0,i1,i2},{0,i1^2,i2^2}}]= i1 i2 (i2-i1)

Det[{{1,1,1,1},{0,i1,i2,i3},{0,i1^2,i2^2,i3^2},{0,i1^3,i2^3,i3^3}}]=
i1 i2 i3 (i3-i2)(i3-i1)(i2-i1)

The next one will be
i1 i2 i3 i4 (i4-i3)(i4-i2)(i4-i1)(i3-i2)(i3-i1)(i2-i1)

The extrapolation should be clear.  The proof, by induction, of the
general form is probably in standard linear algebra texts.  (BTW you can
get rid of the first column and row of your matrix)

Erich

On 13 May 2001, Konstantin L Kouptsov wrote:

>  I am struggling to squeese the following rather simple calculation through the
> existing hardware. The amount of memory (1Gb RAM + 2Gb swap under linux) appears to be
> the resource problem. Any suggestions? How much memory it is supposed to take?
> 
> w={{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 
>    {0, i1, i2, i3, i4, i5, i6, i7, 1, 1 + i8, 1 + i9, 16}, 
>    {0, i1^2, i2^2, i3^2, i4^2, i5^2, i6^2, i7^2, 1, (1 + i8)^2, (1 + i9)^2, 256}, 
>    {0, i1^3, i2^3, i3^3, i4^3, i5^3, i6^3, i7^3, 1, (1 + i8)^3, (1 + i9)^3, 4096}, 
>    {0, i1^4, i2^4, i3^4, i4^4, i5^4, i6^4, i7^4, 1, (1 + i8)^4, (1 + i9)^4, 65536}, 
>    {0, i1^5, i2^5, i3^5, i4^5, i5^5, i6^5, i7^5, 1, (1 + i8)^5, (1 + i9)^5, 1048576}, 
>    {0, i1^6, i2^6, i3^6, i4^6, i5^6, i6^6, i7^6, 1, (1 + i8)^6, (1 + i9)^6, 16777216}, 
>    {0, i1^7, i2^7, i3^7, i4^7, i5^7, i6^7, i7^7, 1, (1 + i8)^7, (1 + i9)^7, 268435456}, 
>    {0, i1^8, i2^8, i3^8, i4^8, i5^8, i6^8, i7^8, 1, (1 + i8)^8, (1 + i9)^8, 4294967296}, 
>    {0, i1^9, i2^9, i3^9, i4^9, i5^9, i6^9, i7^9, 1, (1 + i8)^9, (1 + i9)^9, 68719476736}, 
>    {0, i1^10, i2^10, i3^10, i4^10, i5^10, i6^10, i7^10, 1, (1 + i8)^10, (1 + i9)^10, 1099511627776}, 
>    {0, i1^11, i2^11, i3^11, i4^11, i5^11, i6^11, i7^11, 1, (1 + i8)^11, (1 + i9)^11, 17592186044416}
>   };
> 
> Det[w]
> 
> Konstantin.
> 
> 


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