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Math Help - 3D Vector with homogeneous component

  1. #1
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    Question 3D Vector with homogeneous component

    I know that a 3D Vector is represent with three coordinates. For example V = [3, 2, 5].

    But I don't understand what a 3D vector with homogeneous component is. Does that extra component effect on the norm of a 3D vector? Or is the norm still | V | = \sqrt{3^2 + 2^2 + 5^2}?


    Thank you for some explanation.
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  2. #2
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    Re: 3D Vector with homogeneous component

    Hey Nforce.

    The definition of homogenous (like everything really) is different depending on who is defining it. In many mathematical contexts it refers to something involving a zero but I'm not sure what it means for your situation.

    The norm of a vector should have the same definition for every vector in that space.

    I am taking a look at this:

    Homogeneous coordinates - Wikipedia, the free encyclopedia

    and it says that homogenous co-ordinates refer to co-ordinates based on a projective space.

    In a projective space, you don't have the same norm that you do in a Cartesian space: they are different kinds of spaces and subsequently they have different kinds of metrics, norms, and inner products (if these things exist for that space).
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  3. #3
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    Re: 3D Vector with homogeneous component

    So how can you calculate the norm then? Can you give me some example of a 3D vector with homogenous component and the norm for this 3d vector?
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  4. #4
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    Re: 3D Vector with homogeneous component

    Just to clarify though, are you talking about projective co-ordinate systems?
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  5. #5
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    Re: 3D Vector with homogeneous component

    yes.
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