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Does this just mean .matrices

  1. Aug 26, 2013 #1
    Does this just mean.....matrices

    1. The problem statement, all variables and given/known data

    What does this mean ##βv## but pretend that the angle beta is lower case. This is how my book wrote it.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 26, 2013 #2

    Office_Shredder

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    It's common for vectors to be denoted with bold font and scalars with greek letters, so that's what I would guess, but all that really is is a guess without any context. Can you post the sentence or paragraph where v and beta appear?
     
  4. Aug 26, 2013 #3
    Yep I can.
    Use matrix vector products to show that for any angles theta and beta and any vector v in ## R^2## , ##A_θ(A_βv) = A_θ + βv ##
    Remember that β is lower case on the right side of the equation. I don't know how to make it that way. But read βv as lowercase β.
     
  5. Aug 26, 2013 #4

    Mark44

    Staff: Mentor

    You still haven't given us all of the context; namely, what Aθ and Aβ represent.

    If I had to take a guess, Aθ and Aβ are matrices of some kind, but that assumption isn't consistent with what you have on the right side of the equation: Aθ + βv. Since v is a vector in R2, then βv is, as well, so Aθ must also be a vector in R2. Otherwise the addition is not defined.

    Please clarify what all of the symbols in your equation represent.

    BTW, β is the lower case form of the Greek letter beta. Upper case beta is B.
     
  6. Aug 26, 2013 #5
    Aθ and Aβ are rotation matrices. And what I mean by the βv is that β is sub-scripted before the vector. Why do you give me a warning? My question is one about notation not about actual doing a problem so really there is nothing for me to try. I'm not looking for a solution in the typical sense I just want to know what something means.
     
  7. Aug 26, 2013 #6

    Mark44

    Staff: Mentor

    Your notation is very confusing.
    ##A_θ(A_βv) = A_θ + βv##

    What I think you mean is this:
    ##A_θ(A_βv) = A_{(θ + β)}v##
    The meaning here is that rotating a vector v through an angle β, and then rotating that vector through and angle θ is the same as rotating v through an angle θ + β.

    The notation as you wrote it makes no sense. The right side is the sum of a vector in R2. The right side is the sum of a 2 X 2 matrix and a vector in R2. This addition is not defined.
    From the PF rules:
    If you had included something about what you thought the notation meant, I wouldn't have issued the infraction.
     
  8. Aug 26, 2013 #7
    Mark, I agree with what you wrote "##A_θ(A_βv) = A_{(θ + β)}v##" because this is what I ended up with. I want to also mention that it is not my notation. It is the books notation. I have never seen something written this way. I did not think that I would have to say what I think the notation meant. I think that is a little strict. I understand the rules but it is just a notation question. Do what you want though. Thanks for the help.
     
  9. Aug 26, 2013 #8

    Mark44

    Staff: Mentor

    Did it look like this?
    ##A_θ(A_βv) = A_{θ + β}v##

    On the right side β is a subscript, and maybe that's what you meant when you said "lowercase".
    The rules are what they are, but it's not expected that you will answer any question you post - just give some indication that you have given the question some thought.

    In any case, I will rescind the infraction this time.
     
  10. Aug 26, 2013 #9
    Yes! That is what I was trying to describe! Does that mean the same thing as ##A_θ(A_βv) = A_{(θ + β)}v##???

    OK, I will give more indication of what I'm thinking next time. Thank you.
     
  11. Aug 26, 2013 #10

    Mark44

    Staff: Mentor

    Yes - ## A_{(θ + β)}v## means the same thing as ## A_{θ + β}v##; namely, the matrix of a rotation through and angle of θ + β.
     
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