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Math Help - Clarificatoin on R^n -> R^m

  1. #1
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    Clarificatoin on R^n -> R^m

    Hi, I just wanted to double check something:

    function : R^n -> R^m

    When this says that the function takes a vector n and turns it into vector m, does this mean that we take a vector of size 5 lets say [1, 2, 3, 4, 5] and turn it into another vector also of size 5 e.g. [7, 8, 9, 10, 11]? So in other words, both vectors are the same size/?dimension? so the only thing that the change from n to m signifies is that we're changing the values due to the function/transformation? So it doesn't turn it into a column vector or something? (I may also be confusing and interchanging array and vector).

    This part seems a bit ambiguous for me.
    Last edited by mr fantastic; May 19th 2011 at 02:06 PM. Reason: Moved, re-titled.
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  2. #2
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    Quote Originally Posted by Atomic_Sheep View Post
    Hi, I just wanted to double check something:

    function : R^n -> R^m

    When this says that the function takes a vector n and turns it into vector m, does this mean that we take a vector of size 5 lets say [1, 2, 3, 4, 5] and turn it into another vector also of size 5 e.g. [7, 8, 9, 10, 11]? So in other words, both vectors are the same size/?dimension? so the only thing that the change from n to m signifies is that we're changing the values due to the function/transformation? So it doesn't turn it into a column vector or something? (I may also be confusing and interchanging array and vector).

    This part seems a bit ambiguous for me.
    It means the function takes a vector in R^n and gives you a vector in R^m (of rather it takes an element of R^n to an element of R^m which may be reguarded as taking an n-tuple to am m-tuple), if n != m then the two are of different sizes.

    CB
    Last edited by CaptainBlack; May 19th 2011 at 04:47 AM.
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  3. #3
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    Quote Originally Posted by Atomic_Sheep View Post
    Hi, I just wanted to double check something:

    function : R^n -> R^m

    When this says that the function takes a vector n and turns it into vector m, does this mean that we take a vector of size 5 lets say [1, 2, 3, 4, 5] and turn it into another vector also of size 5 e.g. [7, 8, 9, 10, 11]? So in other words, both vectors are the same size/?dimension? so the only thing that the change from n to m signifies is that we're changing the values due to the function/transformation? So it doesn't turn it into a column vector or something? (I may also be confusing and interchanging array and vector).

    This part seems a bit ambiguous for me.
    Only if it were R^5\to R^5. f: R^n\to R^m takes a vector with n components and turns it into a vector with m components. For example, f(x, y, z)= (3x- y, 2y+ z, x+ z, 3x, 4y) is from R^3 to R^5. It does not matter whether you write it as a column vector or row vector.
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  4. #4
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    Thanks guys, looks like I'll be looking over this again to try and understand it again.
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