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Math Help - Math/Latex to represent getting a minimum value in a 2D range subset

  1. #1
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    Math/Latex to represent getting a minimum value in a 2D range subset

    Hi everyone,

    I would really appreciate some suggestions on what I am trying to say mathematically, and how to write it in Latex.

    I have Data as a 2D table of values. I wish to obtain the minimum value of one particular row while considering the all columns of the table (happens to be zero to pi/2).

    e.g.
    B_max=4 7 4 5
    # # # #
    # # # #
    B_min=2 3 3 2


    what I had originally
     B_{max} = min(Y_i, Y_j) \quad \forall i,j \epsilon Data_{cos  \theta_o^{\prime} = 0}\\ B_{min}  = min(Y_i, Y_j)  \quad \forall i,j  \epsilon Data_{cos \theta_o^{\prime} = cos \theta_{o_{max}}^{\prime}}

    maybe this one is better

     B_{max} = min(Y_{i,{cos \theta_o^{\prime} = 0}} , B_{max})  \forall i \epsilon Data_{[0,\frac{\pi}{2}], [0,0] }


    If you noticed, I am more a programmer than a math guy. But if there is a programmers approach to writing math, i'd be very keen on reading it.
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  2. #2
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    earboth's Avatar
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    Re: Math/Latex to represent getting a minimum value in a 2D range subset

    Quote Originally Posted by lordmule View Post
    Hi everyone,

    I would really appreciate some suggestions on what I am trying to say mathematically, and how to write it in Latex.

    ...

    If you noticed, I am more a programmer than a math guy. But if there is a programmers approach to writing math, i'd be very keen on reading it.
    Maybe this is of some help: Help:Displaying a formula - Wikipedia, the free encyclopedia
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  3. #3
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    Re: Math/Latex to represent getting a minimum value in a 2D range subset

    Quote Originally Posted by earboth View Post
    Thank you for the reply. I did find those math 2 latex useful.

    My initial problem was lacking how to represent, mathematically, a function operating over a subset of 2D data of particular range. I believe that the 2D matrix needs to be defined first:

     Y =  \begin{pmatrix}   y_{1,0} &  \cdots & y_{cos \theta_i, 0} &  \cdots & y_{0, 0} \\   \vdots  &  \ddots & \vdots &  \ddots & \vdots  \\   y_{1, cos \theta_o^{\prime}}   &  \cdots & y_{cos \theta_i, cos \theta_o^{\prime}} &  \cdots & y_{0, cos \theta_o^{\prime}}  \\   \vdots  &  \cdots & \vdots &  \ddots & \vdots  \\   y_{1, cos \theta_{o_{max}}^{\prime}} & \cdots & y_{cos \theta_i ,cos \theta_{o_{max}}^{\prime}} & \cdots & y_{0, cos \theta_{o_{max}}^{\prime}} \end{pmatrix}

    Code:
     Y = 
     \begin{pmatrix}
      y_{1,0} &  \cdots & y_{cos \theta_i, 0} &  \cdots & y_{0, 0} \\
      \vdots  &  \ddots & \vdots &  \ddots & \vdots  \\
      y_{1, cos \theta_o^{\prime}}   &  \cdots & y_{cos \theta_i, cos \theta_o^{\prime}} &  \cdots & y_{0, cos \theta_o^{\prime}}  \\
      \vdots  &  \cdots & \vdots &  \ddots & \vdots  \\
      y_{1, cos \theta_{o_{max}}^{\prime}} & \cdots & y_{cos \theta_i ,cos \theta_{o_{max}}^{\prime}} & \cdots & y_{0, cos \theta_{o_{max}}^{\prime}}
     \end{pmatrix}
    Then define the function on the range with subscripts:

     \begin{array}{l} B_{max} = min_{cos \theta_i, 0}  \;  Y : \theta_i = 0, \cdots , \frac{\pi}{2}  \\ B_{min} = min_{cos \theta_i, cos \theta_{o_{max}}^{\prime}}  \;  Y : \theta_i = 0, \cdots , \frac{\pi}{2} \\ \end{array}

    Code:
    \begin{array}{l}
    B_{max} = min_{cos \theta_i, 0}  \;  Y : \theta_i = 0, \cdots , \frac{\pi}{2}  \\
    B_{min} = min_{cos \theta_i, cos \theta_{o_{max}}^{\prime}}  \;  Y : \theta_i = 0, \cdots , \frac{\pi}{2} \\
    \end{array}
    I believe it is a little clearer. Hopefully the reader will understand.

    Comments welcome!
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