Results 1 to 2 of 2

Math Help - Checking Linear Operators

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Checking Linear Operators

    Given u_x(x,y)-u_y(x+1,y)=xy

    \displaystyle L(u)+L(v)=u_x(x,y)-u_y(x+1,y)+v_x(x,y)-v_y(x+1,y)=(u_x+v_x)(x,y)-(u_y+v_y)(x+1,y)=L(u+v)

    Is that how it should be written, the portion in red?

    Or like this:

    \displaystyle L(u)+L(v)=u_x(x,y)-u_y(x+1,y)+v_x(x,y)-v_y(x+1,y)=u_x(x,y)+v_x(x,y)-(u_y(x+1,y)+v_y(x+1,y))=L(u+v)

    Thanks.

    The color option isn't working. Which line is how it should be shown, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2010
    Posts
    470
    Everything you've written looks fine.

    If you are worried about the expressions like:
    (u_x+v_x)(x,y)

    This is well understood to be addition of functions:
    (f + g)(z) = f(z) + g(z)

    So in this case:
    <br />
f = u_x, g = v_x, z = (x,y)<br />

    which is exactly what you want.

    However, you are missing the step rewriting:

    u_x+v_x = (u + v)_x
    u_y+v_y = (u + v)_y

    This will allow the expression to match the linear operator format exactly without missing an intermediate step.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Operators
    Posted in the Differential Geometry Forum
    Replies: 8
    Last Post: June 7th 2011, 01:05 AM
  2. [SOLVED] PDE Linear Operators
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 29th 2010, 03:27 PM
  3. [SOLVED] Linear Operators
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 27th 2010, 04:52 PM
  4. Linear Operators
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 1st 2009, 11:22 AM
  5. Linear Algebra Question - Linear Operators
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 3rd 2009, 04:33 AM

/mathhelpforum @mathhelpforum