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MathGroup Archive 2004

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Re: Minors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53129] Re: [mg52844] Minors
  • From: Garry Helzer <gah at math.umd.edu>
  • Date: Fri, 24 Dec 2004 05:59:24 -0500 (EST)
  • References: <200412141100.GAA24699@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

If A is the matrix of a linear transformation T on R^n, then 
Minors[A,k] is the matrix of the induced transformation on the k-th  
exterior product--that is the induced transformation on k-vectors 
defined by (using ^ for the wedge product)

T(a1^a2^ . . . ^ak)=T(a1)^T(a2)^ . . . ^T(ak)

I don't know if this is the actual reason, but it is certainly 
convenient.

On Dec 14, 2004, at 3:00 AM, Robert M. Mazo wrote:

> The Minors command gives, as the (i,j) minor af an nxn matrix, what
> ordinary mathematical notation calls the (n-i+1,n-j+1) minor .  I know
> how to work around this.  It is explained on pg. 1195 of The
> Mathematica Book (version 4).  My question here is, why did the
> programmers of Mathematica define Minors this unconventional way?
> They usually had a good reason for their programming quirks, but I
> can't think of a reason for this one.  Can anyone enlighten me?
>
> 	Robert Mazo
> 	mazo at uoregon.edu
>
>
Garry Helzer
gah at math.umd.edu


  • References:
    • Minors
      • From: "Robert M. Mazo" <mazo@uoregon.edu>
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