Results 1 to 6 of 6

Math Help - Determine change of basis matrix

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Determine change of basis matrix

    The question i'm given is to find the change of basis matrix PC<-B . I'm given the bases for both B and C but I'm a bit clueless as to how to solve the question. I figure what they are asking is to find a matrix which turns a vector from the span B to be in the span C instead.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Determine change of basis matrix

    Hey dipsy34.

    I'll start you off with a hint: If x is the vector in the standard basis (identity matrix) then we have c = Cx b = Bx where C and B are the change of basis matrix to go from I (identity) to C or B.

    Hint: Given the hint try getting c in terms of B,C,b and you will have your answer (remember that you can remove a matrix by pre-multiplying it by its inverse matrix).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Re: Determine change of basis matrix

    chiro in your hint are c and b vectors in C respective B or basis?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Determine change of basis matrix

    Yes they are the vectors in the corresponding basis. So b is the vector in basis B and c is the vector in basis C. x is the basis vector in the normal basis R^n.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2008
    Posts
    21

    Re: Determine change of basis matrix

    I think I got it now, I take all the vectors that make up the basis B, b1,b2... ...bk and transforms them using C and the change of basis matrix PC<-B would then consist of the transformed vectors. If they both are instandard basis that is, if not I would have to take: PC<-B = B-1​C?
    Last edited by dipsy34; January 17th 2014 at 11:55 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,419
    Thanks
    1330

    Re: Determine change of basis matrix

    Yes, apply the given linear transformation to each of the basis vectors for the domain space, in turn. Write each result as a linear combination of the given basis vectors for the range space. The coefficients are a column in the matrix.

    (You really have to have ordered bases. The same basis vectors in a different order will give a different matrix.)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Change of coordinate matrix, new basis
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: July 13th 2011, 08:39 PM
  2. Compute the change of basis matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 19th 2011, 10:49 AM
  3. change of basis matrix from B1 to B2.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 13th 2011, 08:42 AM
  4. Orthonormal change of basis matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 24th 2009, 07:10 AM
  5. Change of Basis Matrix
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: June 20th 2009, 12:19 PM

Search Tags


/mathhelpforum @mathhelpforum