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Change of Basis function

• To: mathgroup at smc.vnet.net
• Subject: [mg68949] Change of Basis function
• From: David Boily <dsboily at fastmail.ca>
• Date: Fri, 25 Aug 2006 05:34:59 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Change of Basis function
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Change of Basis function
    • From: "Carl K. Woll" <carlw@wolfram.com>