Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What kind of math notation is this?

  1. Mar 20, 2012 #1
    what kind of math language is this?

    $I\subset \reals$
    $$\gamma_i:I_i\rightarrow M,\quad I_i\subset\reals,\quad i=1,2$$
    $\sigma_{\alpha\beta}$ , let $$\rJ\sigma_{\alpha\beta}:V_{\alpha\beta}\rightarrow \Mat_{n,n}(\reals)$$


    I have seen this notation thrown around in this forum, but I never understood what they mean.
     
    Last edited: Mar 21, 2012
  2. jcsd
  3. Mar 20, 2012 #2
    This is index notation in order to express concisely a list of many equations or functions.
    For example, the first line that you write states that there are two distinct functions γ1 and γ2 such that γ1 maps I1 into M where I1 is a subset of the real numbers and γ2 maps I2 into M where I2 is a subset of the real numbers.
    The arrow notation defines the domain and codomain of the function: I1 is the domain of γ1 and M is the codomain.
    The second set of notation has two indexes on each object; each index is taken to vary independently. For example, if the restrictions on α and β were explicitly given as α = 1, 2 and β = 1, 2, then the expression is a concise way of expressing the following list of expressions:
    [tex]\text{For }\sigma_{11},\text{ let }J\sigma_{11} : V_{11}\rightarrow\text{Mat}_{n, n}(\Re)[/tex]
    [tex]\text{For }\sigma_{12},\text{ let }J\sigma_{12} : V_{12}\rightarrow\text{Mat}_{n, n}(\Re)[/tex]
    [tex]\text{For }\sigma_{21},\text{ let }J\sigma_{21} : V_{21}\rightarrow\text{Mat}_{n, n}(\Re)[/tex]
    [tex]\text{For }\sigma_{22},\text{ let }J\sigma_{22} : V_{22}\rightarrow\text{Mat}_{n, n}(\Re)[/tex]
    In words, the sentence defines a list of 4 functions Jσ_ab that maps each respective space V_ab into the set of nxn matrices with real components. In particular, this means that Jσ_12 takes an element of V_12 as an input and returns an nxn matrix with real components as an output. The explicit operation performed by the function on those elements of V_12 is not specified in this expression.
     
  4. Mar 21, 2012 #3
    alright, let me make this question simpler, what language is this?
    is it latex?
     
  5. Mar 21, 2012 #4
    Yes. You can learn more about how it is used on this forum here.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What kind of math notation is this?
  1. Math notation (Replies: 4)

  2. What is this notation? (Replies: 2)

Loading...