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Describing vectors in n dimensions

  1. Sep 23, 2011 #1
    Recall that A can be broken up into its components x,y, and z. Can You simply add more components to describe any number of dimensions. Where n would be nth dimension?

    A=A_x+ A_y+A_z+⋯A_n
     
  2. jcsd
  3. Sep 23, 2011 #2

    BruceW

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    What's the square symbol for? And why do you have theoretical physics degree in your status thingy? Do you mean you will someday hope to get such a degree? I'm hoping of doing a theoretical phd someday. I didn't know there was such a thing as a purely theoretical undergraduate degree, if that's what youre talking about?

    About the question: If we have a vector A, then it can be written (in some basis) as its components (A1,A2,A3,A4) For a four-dimensional vector, so yeah, there are as many components as there are dimensions.
     
  4. Sep 23, 2011 #3
    For PhD I wrote what I'm striving for. Perhaps that isn't what I should do. :devil: I'll edit it.

    I've only begun my third semester. :)

    Edit: What square symbol?
     
    Last edited: Sep 23, 2011
  5. Sep 23, 2011 #4

    BruceW

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    A=A_x+ A_y+A_z+⋯A_n
    The symbol ⋯ just before A_n it looks like two horizontal lines..
     
  6. Sep 23, 2011 #5
    Oh sorry, that is supposed to be an ellipse (...) that indicates the sequence.
     
  7. Sep 23, 2011 #6

    WannabeNewton

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    You don't write it that way. The components are relative to a basis as Bruce mentioned. A vector can be represented as a linear combination of components relative to said basis vectors so it would be written compactly as [itex]V = V^{\alpha }\vec{e}_{\alpha }[/itex] where the repeated indices imply summation over all possible values the index can take. So, for example, a vector [itex]V \in \mathbb{R}^{n}[/itex] can be written, when equipped with the Cartesian chart, as [itex]V = V^{x}\vec{e_{x}} + ... + V^{n}\vec{e_{n}}[/itex] where [itex]\vec{e_{x}} = (1, 0, ..., 0)[/itex] and similarly for the other basis vectors.
     
  8. Sep 23, 2011 #7
    I have to admit, I am not familiar with that notation. But I will mention that my book stated [itex]A=A_x\widehat{i}+A_y\widehat{j}+A_z\widehat{k}[/itex]. Which is why I simply put:

    [itex] A=A_x\widehat{i}+A_y\widehat{j}+A_z\widehat{k}+...A_n\widehat{t}[/itex]
     
    Last edited: Sep 23, 2011
  9. Sep 23, 2011 #8

    WannabeNewton

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    No that is perfectly correct. It just wasn't in your original post is all.
     
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