Transpose of Matrix

Question: Program to transpose a matrix.

Definition: If A matrix be an m x n matrix, then the matrix obtained by interchanging the rows and columns of A is called the transpose of matrix A. Transpose of the matrix A is denoted by A'. In other words, if A is the order of m x n. then A' is the order of n x m.

Properties of transpose of matrix:

• (A')' = A
• (k A)' = kA'
• (A + B)' = A' +B'
• (AB)' = B' A'

Code Snippet:

1. using System;  
2. public class TransMat  
3. {  
4.     public static void Main()  
5.     {  
6.         int m, n, row, col;  
7.         int[,] matA = new int[10,10];  
8.   
9.         Console.Write("\nEnter the no. of row: ");  
10.         m = Convert.ToInt16(Console.ReadLine());  
11.   
12.         Console.Write("Enter the no. of col: ");  
13.         n = Convert.ToInt16(Console.ReadLine());  
14.   
15.         Console.WriteLine("\nEnter the element in the matrix: ");  
16.         for(row=1; row<=m; row++)  
17.         {  
18.             for(col = 1; col<=n; col++)  
19.             {  
20.                 Console.Write("Matrix A[{0},{1}]: ", row, col );  
21.                 matA[row,col] = Convert.ToInt16(Console.ReadLine());  
22.             }  
23.   
24.             Console.WriteLine();  
25.         }  
26.   
27.         Console.WriteLine("Matrix A :");  
28.         for(row=1; row<=m; row++)  
29.         {  
30.             for(col = 1; col<=n; col++)  
31.             Console.Write("{0:D2} ", matA[row,col]);  
32.   
33.             Console.WriteLine();  
34.         }  
35.   
36.             Console.ReadLine();  
37.   
38.         Console.WriteLine("Matrix A\':");  
39.         for(row=1; row<=n; row++)  
40.         {  
41.             for(col = 1; col<=m; col++)  
42.             Console.Write("{0:D2} ", matA[col,row]);  
43.   
44.             Console.WriteLine();  
45.         }  
46.   
47.         Console.ReadLine();  
48.           
49.     }  
50. }

** Complete code

Description:

To  transpose the matrix we simply change the rows into columns and columns into row.

1. for(row=1; row<=n; row++)  
2.         {  
3.             for(col = 1; col<=m; col++)  
4.             Console.Write("{0:D2} ", matA[col,row]);  
5.   
6.             Console.WriteLine();  
7.         } 

In the above code n is the number of columns which refers the row now and m is the number of row which refers the columns now.

Screenshot of Output:

Read Also:
Interchange operation in Matrix