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MathGroup Archive 2006

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Re: Change of Basis function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68999] Re: Change of Basis function
  • From: "dennis" <dwangsness at earthlink.net>
  • Date: Sat, 26 Aug 2006 02:04:41 -0400 (EDT)
  • References: <ecmh90$9iq$1@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

David,

How about Module[vec_,basis_]:=Inverse[Transpose[basis]].vec

Dennis


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