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MathGroup Archive 2006

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Re: Change of Basis function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68986] Re: [mg68949] Change of Basis function
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sat, 26 Aug 2006 02:04:22 -0400 (EDT)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

Clear[functionX];

functionX[x_?VectorQ, b_List]:=LinearSolve[Transpose[b],x];

functionX[x_, b_?VectorQ]:=Coefficient[x,#]&/@b;

functionX[{1,2,3},{{1,2,0},{0,1,0},{0,0,1}}]

{1,0,3}

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

{f,-b-1,1}


Bob Hanlon

---- David Boily <dsboily at fastmail.ca> 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
> 


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