Thread: Need help with some mathematical notations

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

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

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!

2. Re: Need help with some mathematical notations

Originally Posted by Simplictic
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.

3. Re: Need help with some mathematical notations

Originally Posted by Plato
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.

4. Re: Need help with some mathematical notations

Originally Posted by Simplictic
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 $$...$$ raps like
$$\frac{1}{2} \times 2$$ we get $\frac{1}{2}
\times

2$

But $$\frac{1}{2}\times 2$$ we get $\frac{1}{2}\times2$

5. Re: Need help with some mathematical notations

Originally Posted by Simplictic
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]

6. 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.
$\\$

$\\$
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 $f_{\alpha - k_{l} + e_{d},l}$? $\\$