Results 1 to 7 of 7

Math Help - inner product not by standart basis

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    inner product not by standart basis

    we choose a basis B={v1=(1,0)v2=(1,1)} from R^2
    and define (x,y)_B=x_1y_1+x_2y_2

    why does the prof say that
    x=x_1v_1+x_2v_2
    y=y_1v_1+y_2v_2
    how did he get those formulas?
    and i cant se the structure of our chosen basis here?
    how to see it in thos formulas
    ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: inner product not by standart basis

    Quote Originally Posted by transgalactic View Post
    we choose a basis B={v1=(1,0)v2=(1,1)} from R^2 and define (x,y)_B=x_1y_1+x_2y_2 why does the prof say that x=x_1v_1+x_2v_2 y=y_1v_1+y_2v_2
    Although I don't know what is the final question, taking into account that B is a basis of \mathbb{R}^2 , every x\in \mathbb{R}^2 can be uniquely expressed in the way x=x_1v_1+x_2v_2 . Same considerations for y .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    Re: inner product not by standart basis

    if x=(x1,x2) then x could be represented as x=x_1v_1+x_2v_2

    only if v1=(1,0) v2=(0,1)


    but here we have a different basis not a standart one.
    so our coefficient is not x1 x2

    ??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: inner product not by standart basis

    Perhaps this simple example will help you. Consider x=(5,2) and y=(2,1) . Prove that x=3v_1+2v_2 and y=1v_1+1v_2 . According to the given definition of the inner product we have (x|y)=3\cdot 1+2\cdot 1=5 .
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    Re: inner product not by standart basis

    ok so if i will go by your example
    (x,y)_B=x1y1+x2y2=5*2+2*1=12

    x=(5,2)=5(1,0)+2(1,1)=(7,2)

    i try to follow the logic but i cant understand this term
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: inner product not by standart basis

    Quote Originally Posted by transgalactic View Post
    x=(5,2)=5(1,0)+2(1,1)=(7,2)
    (5,2)\neq (7,2)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    Re: inner product not by standart basis

    i know
    i got here some thing wrong
    just cant understand this basis of inner product
    i am looking for a tutorial with basic examples
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Box and Product basis
    Posted in the Differential Geometry Forum
    Replies: 11
    Last Post: September 25th 2011, 06:29 AM
  2. Orthonormal basis of inner product
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 11th 2010, 03:44 PM
  3. inner product find basis
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 28th 2009, 05:48 AM
  4. Product Basis?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 19th 2009, 08:45 AM
  5. Standart deviation for two groups
    Posted in the Statistics Forum
    Replies: 2
    Last Post: September 8th 2008, 05:10 AM

Search Tags


/mathhelpforum @mathhelpforum