# Matrix Transpose in R

Transpose of a matrix is an operation in which we convert the rows of the matrix in column and column of the matrix in rows. The general equation for performing the transpose of a matrix is as follows.

`Aij = Aji  where i is not equal to j`

Example:

```Matrix M ---> [1, 8, 9
12, 6, 2
19, 42, 3]

Transpose of M
Output --->   [1, 12, 19
8, 6, 42,
9, 2, 3]
```

Transpose of a Matrix can be performed in two ways:

• Finding the transpose by using the t() function

 `# R program for Transpose of a Matrix ` ` `  `# create a matrix with 2 rows  ` `# using matrix() method ` `M <``-` `matrix(``1``:``6``, nrow ``=` `2``)  ` ` `  `# print the original matrix ` `print``(M) ` ` `  `# transpose of matrix ` `# using t() function. ` `t <``-` `t(M)  ` ` `  `# print the transpose matrix ` `print``(t) `

Output:

```     [, 1] [, 2] [, 3]
[1, ]    1    3    5
[2, ]    2    4    6

[, 1] [, 2]
[1, ]    1    2
[2, ]    3    4
[3, ]    5    6
```
• By iterating over each value using Loops:

 `# R program for Matrix Transpose ` ` `  `# create a matrix of 2 rows ` `# using matrix() method. ` `M <``-` `matrix(``1``:``6``, nrow ``=` `2``)  ` ` `  `# print the matrix ` `print``(M) ` ` `  `# create another matrix ` `M2 <``-` `M  ` ` `  `# Loops for Matrix Transpose ` `for` `(i ``in` `1``:nrow(M2)) ` `{    ` `    ``# iterate over each row ` `    ``for` `(j ``in` `1``:ncol(M2)) ` `    ``{  ` `         ``# iterate over each column ` `         ``# assign the correspondent elements ` `         ``# from row to column and column to row. ` `         ``M2[i, j] <``-` `M[j, I]  ` `    ``} ` `} ` ` `  `# print the transposed matrix ` `print``(M2) `

Output:

```     [, 1] [, 2] [, 3]
[1, ]    1    3    5
[2, ]    2    4    6

[, 1] [, 2]
[1, ]    1    2
[2, ]    3    4
[3, ]    5    6
```

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