Q&A

# What does variable in sup represent for matrix?

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I had seen people were representing matrix 2 way.

1. $$\sum_{j=1}^n a_{ij}$$

It is representing a column matrix (vector actually) if we assume $i=1$.

$$\begin{bmatrix}a_{11} & a_{12} & a_{13} & ......\end{bmatrix}$$

1. $$\sum_{j=1}^n a^{ij}$$

What it is representing? At first I thought it was row matrix (vector) since it is opposite of column matrix (vector). But when I was writing the question I couldn't generate a row matrix using the 2nd equation. I confuse more when I see $a_j^{i}$ sometimes there's two variable in sub and sup. $a_{ji}^{kl}$ I don't remember if one of them matches (I meant I am not sure if I write it wrong way).

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