# Sum of columns in a matrix

I want to add columns 1: i of the matrix to get the cumulative sum of each. and then put the results into another matrix

so having:

```
matrix
[,1] [,2] [,3] [,4] [,5]
[1,] A B C D E
[2,] F G H I J
[3,] K L M N O
[4,] P Q R S T
```

become:

```
newmatrix
[,1] [,2] [,3] [,4] [,5]
[1,] A A+B A+B+C A+B+C+D A+B+C+D+E
[2,] F F+G F+G+H F+G+H+I F+G+H+I+J
[3,] K K+L K+L+M K+L+M+N K+L+M+N+O
[4,] P P+Q P+Q+R P+Q+R+S P+Q+R+S+T
```

+3

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2 answers

In theory, you can achieve this by right multiplying by the upper triangular matrix from (size m-by-m where the original matrix is n-by-m)

```
| A B C D | | 1 1 1 1 | | A A+B A+B+C A+B+C+D |
| E F G H | * | 0 1 1 1 | = | E E+F E+F+G E+F+G+H |
| I J K L | | 0 0 1 1 | | I I+J I+J+K I+J+K+L |
| 0 0 0 1 |
```

or

```
| A B C D E | | 1 1 1 1 1 | | A A+B A+B+C A+B+C+D A+B+C+D+E |
| F G H I J | | 0 1 1 1 1 | | F F+G F+G+H F+G+H+I F+G+H+I+J |
| K L M N O | * | 0 0 1 1 1 | = | K K+L K+L+M K+L+M+N K+L+M+N+O |
| P Q R S T | | 0 0 0 1 1 | | P P+Q P+Q+R P+Q+R+S P+Q+R+S+T |
| 0 0 0 0 1 |
```

0

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