Results 1 to 4 of 4

Math Help - Gram-Schmidt process question

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    168

    Gram-Schmidt process question

    Can anyone help me with this? I have to: apply the Gram-Schmidt process to the given subset S of the inner product space V to obtain an orthogonal basis for span(S), normalize it to obtain an orthonormal basis for span(S), and compute the Fourier coefficients of the given vector relative to the orthonormal basis. A lot of words, I know!

    For some reason, the authors of my book thought it would be clever to let us (the students) figure all this out based on just the given theorems, and has not included any good examples. Anyway, here's the info for the problem:

    V = R3
    S = {(1,1,1), (0,1,1), (0,0,1)}
    x = (1,1,2)

    Any help would be MUCH appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    12
    Don't know what is doing that x there, is it another vector?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2009
    Posts
    168
    It's for calculating the Fourier coefficients.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303
    Quote Originally Posted by paupsers View Post
    Can anyone help me with this? I have to: apply the Gram-Schmidt process to the given subset S of the inner product space V to obtain an orthogonal basis for span(S), normalize it to obtain an orthonormal basis for span(S), and compute the Fourier coefficients of the given vector relative to the orthonormal basis. A lot of words, I know!

    For some reason, the authors of my book thought it would be clever to let us (the students) figure all this out based on just the given theorems, and has not included any good examples. Anyway, here's the info for the problem:

    V = R3
    S = {(1,1,1), (0,1,1), (0,0,1)}
    x = (1,1,2)

    Any help would be MUCH appreciated!
    S=\{v_{1}, v_{2}, v_{3}\}

    To find the orthogonal vectors, do the following...

    w_{1}=v_{1}
    w_{2}=v_{2}-proj_{w_{1}}v_{2} as in w_{2}=v_{2}-\frac{<v_{2},w_{1}>}{<w_{1},w_{1}>}w_{1}
    w_{3}=v_{3}-proj_{w_{1}}v_{3}-proj_{w_{2}}v_{3}

    Now, normalize your w_{i}'s...

    u_{i}=\frac{w_{i}}{||w_{i}||}

    Then, the orthonormal basis you are looking for is the set of your u_{i}'s.

    Keep in mind, span(\{v_{1},v_{2},v_{3}\})=span(\{u_{1},u_{2},u_{  3}\}) .

    That's the GOP.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Gram-Schmidt process Help
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: July 10th 2011, 03:06 PM
  2. Gram-Schmidt Process
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 4th 2009, 10:42 PM
  3. Gram Schmidt Process
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 28th 2009, 11:16 PM
  4. Gram-Schmidt Process
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 31st 2009, 02:15 PM
  5. Gram-Schmidt process
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 31st 2009, 03:45 PM

Search Tags


/mathhelpforum @mathhelpforum