Re: Det[]

• To: mathgroup at smc.vnet.net
• Subject: [mg28822] Re: Det[]
• From: "Rasmus Debitsch" <debitsch at zeiss.de>
• Date: Tue, 15 May 2001 00:58:55 -0400 (EDT)
• References: <9dlcge\$o33@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

computing this determinant is quite expensive. A rough estimate of the
number of term of the resulting polynomial will be 11^9.

I'm not sure, but it seems, that after dropping the first row and column,
the determinant is unchanged. Then swapping the columns of ones to the first
column, gives a Vandermonde matrix. The swapping changes the sign of the
determinant. The determinantes of Vandermonde matrices are a well known.

--

Rasmus Debitsch
Carl Zeiss Lithos GmbH
Carl Zeiss Strasse
D-73447 Oberkochen

eMail : debitsch at zeiss.de

"Konstantin L Kouptsov" <klk206 at nyu.edu> schrieb im Newsbeitrag
news:9dlcge\$o33 at smc.vnet.net...
> 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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