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Math Help - Need help with some mathematical notations

  1. #1
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    Need help with some mathematical notations

    Dear all,

    I want to understand a certain algorithm and then try to implement it, but I come across some mathematical notations which make me sick!
    I therefore need help to understand how the following matrix of indexed function f evolves.
    \left[\begin{array}{c} <br />
                    f_{\alpha - k_{1} + e_{d},1}, \dots ,f_{\alpha + k_{1} + e_{d},1}\\<br />
                          .\\<br />
.\\<br />
.\\<br />
                       f_{\alpha - k_{l} + e_{d},L}, \dots ,f_{\alpha + k_{l} + e_{d},L}<br />
                       \end{array}\right]

    where \alpha, k_{l} \in \mathbb{Z}^{D} ; l = 1, \dots , L; \ d = 1, \dots , D and e_{d} is the canonical vector. \\
    Can some one please explain:

    1. How the elements of the matrix obtained? The most difficult thing for me is to understand how the indexing goes. \\
    2. what are the actual elements of \mathbb{Z}^{D} and how does the canonical vector e_{d} look? \\
    3. What kind of operation can I take on f_{\alpha - k_{l} + e_{d},l}? \\

    Any idea is appreciated.

    NB. I'm using TEX to wrap the matrix but still I see <br/>; any one who knows how to fix this is welcome to help!
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  2. #2
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    Re: Need help with some mathematical notations

    Quote Originally Posted by Simplictic View Post
    Dear all,

    I want to understand a certain algorithm and then try to implement it, but I come across some mathematical notations which make me sick!
    I therefore need help to understand how the following matrix of indexed function f evolves.
    \left[\begin{array}{c}f_{\alpha - k_{1} + e_{d},1}, \dots ,f_{\alpha + k_{1} + e_{d},1}\\ .\\.\\.\\f_{\alpha - k_{l} + e_{d},L}, \dots ,f_{\alpha + k_{l} + e_{d},L} \end{array}\right]

    where \alpha, k_{l} \in \mathbb{Z}^{D} ; l = 1, \dots , L; \ d = 1, \dots , D and e_{d} is the canonical vector. \\NB. I'm using TEX to wrap the matrix but still I see <br/>; any one who knows how to fix this is welcome to help!
    You must take out any linefeed
    You can quote reply to see what I have done to fix it.
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  3. #3
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    Re: Need help with some mathematical notations

    Quote Originally Posted by Plato View Post
    You must take out any linefeed
    You can quote reply to see what I have done to fix it.
    Thanks Plato. When I quote reply, can't see the changes you have made.
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  4. #4
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    Re: Need help with some mathematical notations

    Quote Originally Posted by Simplictic View Post
    Thanks Plato. When I quote reply, can't see the changes you have made.
    Do you know what a linefeed is?
    Each time you hit enter inside [tex]... [/tex] raps like
    [tex]\frac{1}{2}
    \times

    2 [/tex] we get \frac{1}{2}<br />
\times<br /> <br />
2

    But [tex]\frac{1}{2}\times 2 [/tex] we get \frac{1}{2}\times2
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  5. #5
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Need help with some mathematical notations

    Quote Originally Posted by Simplictic View Post
    Thanks Plato. When I quote reply, can't see the changes you have made.
    You:



    \left[\begin{array}{c}
    f_{\alpha - k_{1} + e_{d},1}, \dots ,f_{\alpha + k_{1} + e_{d},1}\\
    .\\
    .\\
    .\\
    f_{\alpha - k_{l} + e_{d},L}, \dots ,f_{\alpha + k_{l} + e_{d},L}
    \end{array}\right]



    Plato:


    \left[\begin{array}{c} f_{\alpha - k_{1} + e_{d},1}, \dots ,f_{\alpha + k_{1} + e_{d},1}\\.\\.\\.\\f_{\alpha - k_{l} + e_{d},L}, \dots ,f_{\alpha + k_{l} + e_{d},L}\end{array}\right]
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  6. #6
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    Problem with mathematical notations

    Dear all,

    I want to understand a certain algorithm and then try to implement it, but I come across some mathematical notations which make me sick!
    I therefore need help to understand how the elements of the following matrix of indexed function f evolve:
    \\

    \left[\begin{array}{c} f_{\alpha - k_{1} + e_{d},1}, \dots ,f_{\alpha + k_{1} + e_{d},1}\\.\\.\\.\\f_{\alpha - k_{l} + e_{d},L}, \dots ,f_{\alpha + k_{l} + e_{d},L}\end{array}\right],

    where \alpha, k_{l} \in \mathbb{Z}^{D} ; l = 1, \dots ,  L; \ d = 1, \dots , D and e_{d} is the canonical vector.
    \\

    Can some one please explain:
    \\

    1. How the elements of the matrix obtained? The most difficult thing for me is to understand how the indexing goes. \\
    2. What are the actual elements of \mathbb{Z}^{D} and how does the canonical vector e_{d} look? \\
    3. What kind of operation can I take on f_{\alpha - k_{l} + e_{d},l}? \\

    Any idea is welcome.
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  7. #7
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    Re: Need help with some mathematical notations

    Thanks Also sprach Zarathustra.
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