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MathGroup Archive 2006

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Re: Change of Basis function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68990] Re: [mg68949] Change of Basis function
  • From: "Carl K. Woll" <carlw at wolfram.com>
  • Date: Sat, 26 Aug 2006 02:04:27 -0400 (EDT)
  • References: <200608250934.FAA09206@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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.
> 
> David Boily
> Center for Intelligent Machines 
> Mcgill University

To answer your second question, you can use LinearEquationsToMatrices 
from the LinearAlgebra`MatrixManipulation` package, or just use 
Developer`LinearExpressionToMatrix directly:

In[1]:=
Developer`LinearExpressionToMatrix[f x1-b x2+x3-x2,{x1,x2,x3}]

Out[1]=
{{{f,-b-1,1}},{0}}

Carl Woll
Wolfram Research


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