Matrix notation (sigma of matrix) (refer to a number in matrix)

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If I define a matrix to be equal to x, may I then refer to a specific number in the matrix by index like so:

$$x=\begin{bmatrix}0,01\\0,05\\0,30\end{bmatrix}~~~~x_1+x_2=0,06$$


Also, can you do the following?

$$\sum \begin{bmatrix}0,01\\0,05\\0,30\end{bmatrix}=0,36$$

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Yes, you can refer specific entries in matrix, for example

$$A=\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{bmatrix} $$ in here $a_{11} = 1$, $a_{22} = 5$, $a_{31} = 7$

In general the notation is $a_{ij}$ where the first subscript is the row number and the second is the column number.


If you want to sum all the elements in a column 1 you can do

$\sum_{i = 1}^n a_{i1}$ where n is the number of elements in first column.

And for j:th column it's $\sum_{i = 1}^n a_{ij}$ where n is the number of elements in j:th column.

For rows you just sum through the columns instead of rows, and if you want to sum all elements of the matrix the sum is

$\sum_{i = 1}^n \sum_{j = 1}^k a_{ij}$ where the n is number of rows and k is number of columns.

I hope this helps, this is my first answer on stackexchange.