Results 1 to 5 of 5

Math Help - matrix and basis

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    4

    Red face matrix and basis

    Consider a) f1=1, f2=sinx , f3=cosx
    b) f1=1, f2=ex , f3=e2x
    c)f1=e2x , f2=xe2x f3=x2e2x
    in each part B={f1,f2,f3} is a basis for a subspace V of the vector space.
    Find the matrix with respect to B of the differentiation operator D:V→V
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1

    Re: matrix and basis

    Quote Originally Posted by bernoli View Post
    Consider a) f1=1, f2=sinx , f3=cosx
    b) f1=1, f2=ex , f3=e2x
    c)f1=e2x , f2=xe2x f3=x2e2x
    in each part B={f1,f2,f3} is a basis for a subspace V of the vector space.
    Find the matrix with respect to B of the differentiation operator D:V→V
    What have you been able to do on this problem so far?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,419
    Thanks
    1856

    Re: matrix and basis

    Apply the operator to each basis function in turn and write the result as a linear combination of the basis functions. The coefficients in that linear combination form one column in the matrix representation.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2011
    Posts
    4

    Re: matrix and basis

    f '=0 f'2=cos x f'3=-sinx
    0 0 0

    A= 0 cosx 0

    0 0 -sinx A is matrix


    is this okay
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,419
    Thanks
    1856

    Re: matrix and basis

    No, the matrix consists of the coeficients, not the functions.

    f1(x)= 1 so f1'(x)= 0(1)+ 0(sin(x))+ 0(cos(x)): <0, 0, 0>

    f2(x)= sin(x) so f2'(x)= 0(1)+ 0(sin(x))+ 1(cos(x)): <0, 0, 1>

    f3(x)= cos(x) so f2'(x)= 0(1)+ (-1)(sin(x))+ 0(cos(x)): <0, -1, 0>

    The matrix is
    \begin{bmatrix}0 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0\end{bmatrix}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The basis of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 9th 2012, 04:18 AM
  2. change of basis matrix from B1 to B2.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 13th 2011, 09:42 AM
  3. Change of Basis Matrix
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: June 20th 2009, 01:19 PM
  4. Basis Matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 22nd 2008, 04:38 PM
  5. basis for matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 28th 2007, 05:04 PM

Search Tags


/mathhelpforum @mathhelpforum