How can I write a set of equations in summation form?

Question

I have a system of equations as follows:

\begin{align} & A_1^{11} + A_1^{12} + A_1^{13} + \cdots + A_1^{1n}=X \\[8pt] & A_1^{21} + A_1^{22} + A_1^{23} + \cdots+ A_1^{2n}=X \\[8pt] & \qquad \vdots \\[8pt] & A_1^{n1} + A_1^{n2} + A_1^{n3} + \cdots + A_1^{nn}=X \\[8pt] & A_2^{11} + A_2^{12} + A_2^{13} + \cdots + A_2^{1n}=X \\[8pt] & \qquad\vdots \\[8pt] & A_2^{n1} + A_2^{n2} + A_2^{n3} + \cdots + A_2^{nn}=X \\[8pt] & \qquad\vdots \\[8pt] & A_m^{11} + A_m^{12} + A_m^{13} + \cdots + A_m^{1n}=X \\[8pt] & \qquad\vdots \\[8pt] & A_m^{n1} + A_m^{n2} + A_m^{n3} + \cdots + A_m^{nn}=X \end{align}

How can I write these equations in a summation form?

Answer 1

You could write $$\sum_{i=1}^nA_j^{ki}=X$$ with the point being that this equation is true for all $j,k$. You have $mn$ equations here, each one summing over one of the indices on $A$.