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)
• 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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