Results 1 to 10 of 10

Math Help - dot products

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    127

    dot products

    Simplify ||x+y||^2 -||x||^2-||y||^2 using dot products
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    <x+y,x+y>=<x,x+y>+<y,x+y>=<x,x>+<x,y>\cdots
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Continuing

    <x+y,x+y>=||x||^2+2<x,y>+||y||^2
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by Taurus3 View Post
    Simplify ||x+y||^2 -||x||^2-||y||^2 using dot products
    I wish helpers knew what is needed.
    \left\| {x + y} \right\|^2  = \left( {x + y} \right) \cdot \left( {x + y} \right) = x \cdot x + 2x \cdot y + y \cdot y =
    \left\| x \right\|^2  + 2x \cdot y + \left\| y \right\|^2
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by Plato View Post
    I whish helpers knew what is needed.
    \left\| {x + y} \right\|^2  = \left( {x + y} \right) \cdot \left( {x + y} \right) = x \cdot x + 2x \cdot y + y \cdot y =
    \left\| x \right\|^2  + 2x \cdot y + \left\| y \right\|^2
    That makes no sense since I supplied that exact answer. Additionally, I gave him/her the opportunity to finish it themselves.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2010
    Posts
    127
    oh wow. That was pretty confusing haha.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Dec 2010
    Posts
    470
    Quote Originally Posted by Taurus3 View Post
    oh wow. That was pretty confusing haha.
    Taurus3, all the math in the above posts are correct, and trying to help you reach the answer.
    What parts are you confused about?

    As a side note, you can also find the value of ||x+y||^2 -||x||^2-||y||^2 using the law of cosines.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by dwsmith View Post
    That makes no sense since I supplied that exact answer.
    I am sorry but I don't see anything about a dot product in your reply.
    Did I miss something?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Your solutions are wrong since you didn't transpose.

    The standard inner product for \mathbb{R} is the scalar product

    <x,y>=x^T\cdot y.

    x_{n,1}\cdot x_{n,1}=DNE \ \ \mbox{but} \ x_{1,n}\cdot x_{n,1}=\alpha \ \ \alpha\in\mathbb{R}

    You are only correct if the vectors are 1,1 but you can't make that assumption.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dwsmith View Post
    Your solutions are wrong since you didn't transpose.

    The standard inner product for \mathbb{R} is the scalar product

    <x,y>=x^T\cdot y.

    x_{n,1}\cdot x_{n,1}=DNE \ \ \mbox{but} \ x_{1,n}\cdot x_{n,1}=\alpha \ \ \alpha\in\mathbb{R}

    You are only correct if the vectors are 1,1 but you can't make that assumption.
    Dot product is not a matrix product of a row and column vector (so no transpose required). Plato's approach is correct and it is the approach that is expected (Your inner product is not a "dot" product as required by the question. You are assuming more knowledge on the part of the OP and so what you post is probably gobbledygook to them)

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Dot products
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: July 1st 2011, 04:32 PM
  2. Inner Products
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 28th 2011, 06:40 PM
  3. ...norm takes products to products.
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 23rd 2010, 09:55 PM
  4. Inner Products
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: April 17th 2010, 09:34 PM
  5. Inner products
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 4th 2007, 08:36 PM

Search Tags


/mathhelpforum @mathhelpforum