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MathGroup Archive 2006

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Re: Change of Basis function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69010] Re: Change of Basis function
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Sat, 26 Aug 2006 02:04:58 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 8/25/06 at 5:34 AM, dsboily at fastmail.ca (David Boily) wrote:

>I would like to know if there is a function capable of giving as
>output the representation of a vector in a given basis. For example:

>FunctionX[{1,2,3}, {{1,2,0},{0,1,0},{0,0,1}}]

>(where the first argument is the vector and the second the basis)

>would yield

>{1,0,3}

>and

>FunctionX[f x1 - b x2 + x3 - x2, {x1,x2,x3}]

>would yield

>{f, -b-1, 1}

>I'm more interested in the second case, obviously, because the first
>one can be achieved with a simple matrix multiplication.

Take a look at CoefficientArrays in the help browser. That is your specific example can be done as:

In[24]:=
Normal@Last@CoefficientArrays[f x1-b x2+x3-x2,{x1,x2,x3}]

Out[24]=
{f,-b-1,1}
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