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Math Help - Matrix help

  1. #1
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    Aug 2011
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    Matrix help

    Lets say that I have some matrix A,with values:
    [1 0 0;
    0 0 0;
    0 0 0;];

    How do I mathematically alter the matrix to change from its current for to (s=0 is the initial iteration) :
    [1 1 1;
    1 1 1;
    1 1 1;];
    s=1

    [1 2 2;
    2 2 2;
    2 2 2;];
    s=2

    [1 2 3;
    2 2 3;
    3 3 3;];
    s=3

    My first thought: I can think of any point on the matrix as the vertex of some inverted pyramid ( abs(x-i) + abs(y-j)), and place the pyramid on top of that point, and pull it down. At each step down, the elements of matrix A that grow become farther and farther apart. But apparently, I am wrong. Any tips? Once again, you guys rock.
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  2. #2
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    Joined
    Aug 2011
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    Re: Matrix help

    Attachment 23697

    It makes more sense now that I thik about it. As x and y increase, the values of the matrix go up accordingly. I attached a picture of what the matrix looks like at each iteration (via color) the center color represents 1, and each iteration outside of it increases by 1 (i.e., black=1, grey = 2, brown = 3, red =4, etc). each value outside of the initial value increases linearly, but I cannot for the life of me figure out how to apply a function like that
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  3. #3
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    Re: Matrix help

    (Sorry for the repeated responses to my own post, I am just spitting out thoughts as a I go).

    not sure if this helps: (just derived it :P)
    (abs(x*cos(45)-y*sin(45))+abs(x*sin(45)+y*cos(45))) = z

    vertices start at z.

    Made my equation for the square more 'pretty':
    z = (abs(x-y))/sqrt(2)+(abs(x+y))/sqrt(2)
    Last edited by breakeron; April 23rd 2012 at 02:33 PM.
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