- Print the original matrix
- Print the transpose matrix
- Print the product of the original matrix and the transpose

## Transpose of a Matrix

To “transpose” a matrix, swap the rows and columns. We put a “T” in the top right-hand corner to mean transpose:

# How to Multiply Matrices

A Matrix is an array of numbers:

A Matrix

(This one has 2 Rows and 3 Columns)

To multiply a matrix by a single number is easy:

2×4=8 | 2×0=0 |

2×1=2 | 2×-9=-18 |

We call the number (“2” in this case) a **scalar**, so this is called “scalar multiplication”.

## Multiplying a Matrix by Another Matrix

But to multiply a matrix **by another matrix** we need to do the “**dot product**” of rows and columns … what does that mean? Let us see with an example:

To work out the answer for the **1st row** and **1st column**:

The “Dot Product” is where we

multiply matching members, then sum up:(1, 2, 3) • (7, 9, 11) = 1×7 + 2×9 + 3×11 = 58

We match the 1st members (1 and 7), multiply them, likewise for the 2nd members (2 and 9) and the 3rd members (3 and 11), and finally sum them up.

Here it is for the 1st row and **2nd column**:

(1, 2, 3) • (8, 10, 12) = 1×8 + 2×10 + 3×12 = 64

We can do the same thing for the **2nd row** and **1st column**:

(4, 5, 6) • (7, 9, 11) = 4×7 + 5×9 + 6×11 = 139

And for the **2nd row** and **2nd column**:

(4, 5, 6) • (8, 10, 12) = 4×8 + 5×10 + 6×12 = 154

And we get:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 |
import java.io.*; public class Transpose_Multiply { public static void main()throws IOException { BufferedReader r = new BufferedReader(new InputStreamReader(System.in)); int m, n; System.out.println("Enter the number of rows:"); m = Integer.parseInt(r.readLine()); System.out.println("Enter the number of columns:"); n = Integer.parseInt(r.readLine()); int a[][] = new int[m][n], b[][] = new int[n][m], i, j, s=0, k; System.out.println("Enter the values for the array:"); for(i=0;i<m;i++) { for(j=0;j<n;j++) { a[i][j] = Integer.parseInt(r.readLine()); b[j][i] = a[i][j]; } } int c[][] = new int[m][m]; for(i=0;i<m;i++) { for(j=0;j<m;j++) { s=0; for(k=0;k<n;k++) { s+=a[i][k]*b[k][j]; } c[i][j] = s; } } //Printing the various arrays System.out.println("Original Array:"); for(i=0;i<m;i++) { for(j=0;j<n;j++) { System.out.print(a[i][j]+"t"); } System.out.println(); } //Printing the various arrays System.out.println("Transpose Array:"); for(i=0;i<n;i++) { for(j=0;j<m;j++) { System.out.print(b[i][j]+"t"); } System.out.println(); } //Printing the various arrays System.out.println("Multiplied Array:"); for(i=0;i<m;i++) { for(j=0;j<m;j++) { System.out.print(c[i][j]+"t"); } System.out.println(); } } } |

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