Neural network Equation question I am looking at an example for the activation function $a_1$.
Why does the equation look like $\Theta_{10}x_0 + \Theta_{11}x_1 + \Theta_{12}x_2 + \Theta_{13}x_3$
instead of
$\Theta_{10}x_0 + \Theta_{11}x_1 + \Theta_{21}x_2 + \Theta_{31}x_3$?
My understanding is that all input nodes will contribute to the computation of activation value of $a_1$. And hence, shouldn't $\Theta_{xy}$ be the value from $x$ to $y$? Which in this case of $\Theta_{21}$ be from Node $2$ in first layer to Node $1$ in second layer. Am I misunderstanding something?
This is the url 

 A: To quote the very page the image is from:
$\Theta_{ji}^{(l)}$


*

*$j$ (first of two subscript numbers)= ranges from $1$ to the number of units in layer $l+1$

*$i$ (second of two subscript numbers) = ranges from $0$ to the number of units in layer $l$

*$l$ is the layer you're moving FROM



I guess the choice for this is to be able to write it with matrices:
$
\underbrace{
\begin{pmatrix}
\Theta_{00} & \Theta_{01} & \Theta_{02} & \Theta_{03} \\
\Theta_{10} & \Theta_{11} & \Theta_{12} & \Theta_{13} \\
\Theta_{20} & \Theta_{21} & \Theta_{22} & \Theta_{23} \\
\end{pmatrix} }_{\Huge\Theta_{ji}}
*
\begin{pmatrix}
x_{0} \\
x_{1} \\
x_{2} \\
x_{3}
\end{pmatrix} 
=
\begin{pmatrix}
\Theta_{00}x_0 & \Theta_{01}x_1 & \Theta_{02}x_2 & \Theta_{03}x_3 \\
\Theta_{10}x_0 & \Theta_{11}x_1 & \Theta_{12}x_2 & \Theta_{13}x_3 \\
\Theta_{20}x_0 & \Theta_{21}x_1 & \Theta_{22}x_2 & \Theta_{23}x_3 \\
\end{pmatrix} 
\begin{matrix}
(\text{input }a_1) \\
(\text{input }a_2) \\
(\text{input }a_3) \\
\end{matrix} 
$
$x_0$ is bias by the way.
With $\Theta_{ij}$ you'd have $x^T\Theta_{ij}$ where every column $c$ would be input to $a_c$ but its custom to have the vector after the matrix.
