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Matrices ?

  1. Jun 20, 2003 #1

    drag

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    Greetings !

    Can anyone please explain to me, preferably with as
    little math and as much theory as possible , how
    matrices work in terms of forms and dimensions and what's
    the relevant mechanism ?

    I mean, I used to program Star Trek spaceships for a computer
    game I once made using matrices. But, nobody ever explained
    to me how and why it works, those were just meaningless tables
    with sprecific relevant operators to me. I also know the
    whole addition/multiplication/other operations stuff(though
    I can hardly remember it now), but not how and why it works for geometrical forms in various dimensions and stuff.

    Thanks ! :smile:

    Live long and prosper.
     
  2. jcsd
  3. Jun 20, 2003 #2

    HallsofIvy

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  4. Jun 23, 2003 #3
    OK so maybe this is a response for a restricted area of matices use but here goes.
    I program in OpenGL and I think the other 3D programming stuff has the same principles. To make a 3D scene you have to use coordinate transformation. These transformations (translation, rotation, scaling) can be writen as a linear sistem between the coordinates in the old reference system, and the coordinates in the new reference system. Any linear eqation system can be expressed in a matriceal form. So this is one of the reasons you use matrices. Also basic matrix operations are easy to program.
     
  5. Jun 23, 2003 #4
    Or, in other words ...
    You can do all the world transformation without matrices, it is only that matrices is a convinient way to save points, data, and transformations.
    (i learned that while trying to learn Direct3D)
     
  6. Jun 23, 2003 #5
    One of the most interesting things about matrices are than, due to the method of multiplication A * B is not necessarily the same as B * A.
     
  7. Jun 23, 2003 #6
    Yep, Matrix multiplication is noncommutative and I know some people who failed exams because of it (even though the teacher had mentioned many times).
     
  8. Jun 23, 2003 #7
    true, true....
    that's why in OpenGL a rotation, followed by a translation doesn't have the same result as a translation followed by a rotation. To do that you have to make some matrix multiplication and since it's not commutative the results are dependent of the order in which you multiply.
     
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