Transpose of a Matrix in C

Transpose of a matrix is a matrix that is obtained by swapping the rows and columns of the given matrix or vice versa, i.e., for the given matrix the elements in rows are interchanged with the elements in columns. For any given matrix A its transpose is denoted as A^t, or A^T.

Note: The transpose of an m × n matrix will result in an n × m matrix.

Transpose of a Square Matrix

Square matrices are matrices that have an equal number of rows and columns. For any square matrix A_n×n, its transpose has the same order i.e., the transpose of A, A^t has order n × n. The rows and columns are interchanged in the transpose of a square matrix.

Transpose of the matrix:
1 4 7 
2 5 8 
3 6 9 

Complexity Analysis

• Time Complexity: O(n²)
• Auxiliary Space: O(n ²)

Transpose of a Rectangular Matrix

The transpose of a rectangular matrix is formed by turning its rows into columns (and columns into rows).

If the original matrix is of size m × n, its transpose will be of size n × m. In other words, the element at position [i][j] moves to [j][i] in the transposed matrix.

Transpose of the matrix:
1 4 
2 5 
3 6 

Complexity Analysis

• Time Complexity: O(n*m)
• Auxiliary Space: O(n*m)