Matrix programs

Program to calculate the addition of 2 matrices

Matrix a = [1, 1, 1]
           [4, 5, 6]
           [1, 2, 3]
 
matrix b = [1, 1, 1]
           [-2, 3, 1]
           [1, 0, 1]

Addition of two matrices: [2 2 2]
                          [2 8 7]
                          [2 2 4]

Program to calculate the subtract two matrices

Matrix a = [4, 5, 5]
           [3, 0, 1]
           [1, 2, 3]

Matrix b = [2, 0, 3]
           [2, 3, 1]
           [0, 1, 1]

Subtraction of two matrices:
[2  5  2]
[1 -3 0]
[1  1  2]

Program to determine whether a given matrix is an identity matrix.

A matrix is said to be the identity matrix if it is the square matrix in which elements of principle diagonal are ones, and the rest of the elements are zeroes.

[1, 0, 0]
[0, 1, 0]
[0, 0, 1]

MATRIX IS AN IDENTITY MATRIX

Program to determine whether a given matrix is a sparse matrix.

A matrix is said to be sparse matrix if most of the elements of that matrix are 0. It implies that it contains very less non-zero elements.

For the matrix to be sparse, count of zero elements present in an array must be greater than size/2.

Matrix  = [4, 0, 0]
          [0, 5, 0]
          [0, 0, 6]

MATRIX IS AN SPARSE MATRIX

Program to determine whether two matrices are equal

Program to display the lower triangular matrix
(Lower triangular matrix is a square matrix in which all the elements above the principle diagonal will be zero)

Matrix  = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

LOWER TRIANGULAR MATRIX 
[9, 0, 0]
[6, 5, 0]
[3, 2, 1]

Program to display the upper triangular matrix
(Upper triangular matrix is a square matrix in which all the elements below the principle diagonal will be zero)

Matrix  = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

UPPER TRIANGULAR MATRIX 
[9, 8, 7]
[0, 5, 4]
[0, 0, 1]

Program to display the even number in the matrix

Matrix  = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

EVEN NUMBER IN MATRIX 
   8  
6     4
   2

Program to display the odd number in the matrix

Matrix  = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

ODD NUMBER IN MATRIX 
9     7  
   5  
3     1

Program to print frequency of even number in the matrix

Matrix  = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

Frequency of even number in matrix:4

Program to print frequency of odd number in the matrix

Matrix  = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

Frequency of odd number in matrix:5

Program to print frequency of odd and even number in the matrix

Matrix  = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

Frequency of odd number in matrix:5
Frequency of even number in matrix:4

Program to find product of two matrices.
Two matrices can be multiplied if and only if The number of columns present in the first matrix should be equal to the number of rows present in the second matrix.

Matrix A = [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]
          
Matrix B = [1, 2, 3]
           [4, 5, 6]
           [7, 8, 9]

PRODUCT OF TWO  MATRICES 
90  114  138
54  69   84
18  24   30

Program to find sum of all number in the matrix

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SUM OF ALL NUMBER IN THE MATRIX:45

Program to find sum of each row in the matrix

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SUM OF EACH ROW IN THE MATRIX
24
15
6

Program to find sum of each column in the matrix

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SUM OF EACH COLUMN IN THE MATRIX
18  15  12

Program to find the transpose of a given matrix

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

TRANSPOSE
[9, 6, 3]
[8, 5, 2]
[7, 4, 1]

Program to check whether the matrix is symmetric matrix
(symmetric matrix is a square matrix that is equal to its transpose)

Matrix =  [3, -2, 4]
          [-2, 6, 2]
          [4, 2, 3]

TRANSPOSE:
[3, -2, 4]
[-2, 6, 2]
[4, 2,  3]
THE MATRIX IS SYMMETRIC MATRIX

Program to check whether the matrix is orthogonal matrix
(To determine if a matrix is orthogonal, we need to multiply the matrix by it's transpose, and see if we get the identity matrix.)

Matrix =  [1,0,0]
          [0,1,0]
          [0,0,1]

TRANSPOSE:
[1,0,0]
[0,1,0]
[0,0,1]
PRODUCT OF TRANSPOSE MATRIX AND ORIGINAL MATRIX:
[1,0,0]
[0,1,0]
[0,0,1]
MATRIX IS ORTHOGONAL MATRIX

Program to print right and left diagonal of matrix(principal diagonal matrix).

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

DIAGONALS OF MATRIX
9     7
   5
3     1

Program to print elements that are not on diagonals of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

ELEMENTS NOT ON DIAGONALS OF MATRIX
   8   
6     4
   2

Program to print sum of elements that are on diagonals of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SUM OF DIAGONAL MATRIX:25

Program to print boundary elements of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

BOUNDARY ELEMENTS OF MATRIX
9  8  7 
6     4
3  2  1

Program to print non-boundary elements of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

NON-BOUNDARY ELEMENTS OF MATRIX
 
  5

Program to find sum of non-diagonal elements of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SUM OF NON-DIAGONAL ELEMENTS OF MATRIX:20

Program to find sum of boundary elements of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SUM OF BOUNDARY ELEMENTS OF MATRIX:40

Program to find sum of non-boundary elements of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SUM OF NON-BOUNDARY ELEMENTS OF MATRIX:5

Program to find largest element of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

LARGEST ELEMENT OF MATRIX:9

Program to find smallest element of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SMALLEST ELEMENT OF MATRIX:1

Program to find largest element in diagonals of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

LARGEST ELEMENT IN DIAGONALS OF MATRIX:9

Program to find smallest element in diagonals of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SMALLEST ELEMENT IN DIAGONALS OF MATRIX:1

Program to find largest element in boundary elements of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

LARGEST ELEMENT IN BOUNDARY ELEMENT OF MATRIX:9

Program to find smallest boundary elements of matrix .

Matrix =  [9, 8, 7]
          [6, 5, 4]
          [3, 2, 1]

SMALLEST ELEMENT IN BOUNDARY ELEMENT OF MATRIX:1

Program to sort matrix in ascending order .

Matrix =  [5, 2, 7]
          [9, 6, 4]
          [3, 8, 1]

SORTED MATRIX
1  2  3
4  5  6
7  8  9

Program to sort matrix in descending order .

Matrix =  [5, 2, 7]
          [9, 6, 4]
          [3, 8, 1]

SORTED MATRIX
9  8  7
6  5  4
3  2  1

Program to sort boundary elements in ascending order in a matrix

Matrix =  [5, 2, 7]
          [9, 6, 4]
          [3, 8, 1]

SORTED MATRIX
1  2  3
4  6  5
7  8  9

Program to sort boundary elements in descending order in a matrix

Matrix =  [5, 2, 7]
          [9, 6, 4]
          [3, 8, 1]

SORTED MATRIX
9  8  7
5  6  4
3  2  1

Program to sort non-boundary elements of matrix in ascending order .

Matrix =  [5, 2, 9, 8, 7]
          [9, 6, 4, 2, 3]
          [3, 8, 1, 3, 9]
          [1, 2, 3, 4, 5]

SORTED MATRIX
[5, 2, 9, 8, 7]
[9, 1, 2, 3, 3]
[3, 4, 6, 8, 9]
[1, 2, 3, 4, 5]

Program to sort non-boundary elements of matrix in descending order .

Matrix =  [5, 2, 9, 8, 7]
          [9, 6, 4, 2, 3]
          [3, 8, 1, 3, 9]
          [1, 2, 3, 4, 5]

SORTED MATRIX
[5, 2, 9, 8, 7]
[9, 8, 6, 4, 3]
[3, 3, 2, 1, 9]
[1, 2, 3, 4, 5]

Program to print matrix in spiral order

Matrix
[1, 2, 3]
[4, 5, 6]
[7, 8, 9]

spiral
1 2 3 6 9 8 7 4 5

Program to print matrix in spiral order in anticlockwise

Matrix
[1, 2, 3]
[4, 5, 6]
[7, 8, 9]

spiral
1 4 7 8 9 6 3 2 5

Program to row wise sorting matrix in ascending order

Matrix
[3, 20, 1]
[13, 5, 4]
[9, 19, 7]

SORTED MATRIX
1 3 20
4 5 13
7 9 19

Program to row wise sorting matrix in descending order

Matrix
[3, 20, 1]
[13, 5, 4]
[9, 19, 7]

SORTED MATRIX
20 3 1
13 5 4
19 9 7

Program to column wise sorting matrix in ascending order

Matrix
[3, 20, 1]
[13, 5, 4]
[9, 19, 7]

SORTED MATRIX
3  5  1
9  19 4
13 20 7

Program to column wise sorting matrix in descending order

Matrix
[3, 20, 1]
[13, 5, 4]
[9, 19, 7]

SORTED MATRIX
13 20 7
9  19 4
3  5  1

Program to search element in the given matrix

ENTER THE ROW
3
ENTER THE COLUMN
3
ENTER THE ELEMENTS IN ARRAY
1
2
3
4
5
6
1
7
8
ENTER THE ELEMENT TO BE SEARCHED
1
SEARCHED ELEMENT FOUND row:1 column1
SEARCHED ELEMENT FOUND row:3 column1

Shift rows of matrix in cyclic order that is, Swap 1st row with 2nd row, 2nd row with 3rd and last row with 1st.Display the Original array and array after swapping.

OUTPUT:
Enter Number of rows:
4
Enter Number of columns:
4
Enter Elements in Array:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Original Array:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
Array After Cycling row :
13 14 15 16 
1 2 3 4 
5 6 7 8 
9 10 11 12

Swap first and last row of 2D Integer array

OUTPUT:
Enter Number of rows:
4
Enter Number of columns:
4
Enter Elements in Array:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Original Array:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
Array after swapping first and last row:
13 14 15 16 
5 6 7 8 
9 10 11 12 
1 2 3 4

Print elements below the left diagonal of the integer matrix.

Enter size of array:
4
Enter Elements in Array:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Original Matrix:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
Elements Below the Left diagonal of Matrix:
        
5       
9 10     
13 14 15

Print elements below the right diagonal of the integer matrix.

Enter size of Matrix:
4
Enter Elements in Matrix:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Original Matrix:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
elements Below right Diagonal Matrix:
        
      8 
    11 12 
  14 15 16

Print elements above the right diagonal of the integer matrix.

Enter size of Matrix:
4
Enter Elements in Matrix:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Original Matrix:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
Elements Above right Diagonal Matrix:
1 2 3   
5 6     
9

Multiply two matrices and display both the original matrices and resultant matrix

Enter Row size of 1st matrix:
2
Enter Column size of 1st matrix:
3
Enter Row size of 2nd matrix:
3
Enter Column size of 2nd matrix:
4
Enter Elements in First Matrix:
1
2
3
4
5
6
Enter Elements in Second Matrix:
1
2
3
4
5
6
7
8
9
10
11
12
Matrix 1:
1 2 3 
4 5 6 
Matrix 2:
1 2 3 4 
5 6 7 8 
9 10 11 12 
Matrix 1 * Matrix 2:
38 44 50 56 
83 98 113 128

Print Product of elements of each row and column in integer matrix.

Enter size of integer Matrix:
4
Enter Elements in Matrix:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Elements in Matrix:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
The product of elements of row 1 is=24
The product of elements of row 2 is=1680
The product of elements of row 3 is=11880
The product of elements of row 4 is=43680
The product of elements of Column 1 is=585
The product of elements of Column 2 is=1680
The product of elements of Column 3 is=3465
The product of elements of Column 4 is=6144

Print largest element of each row in integer matrix.

Enter size of integer matrix:
4
Enter Elements in matrix:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Elements in matrix:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
The Largest value of row 1 is=4
The Largest value of row 2 is=8
The Largest value of row 3 is=12
The Largest value of row 4 is=16

Print largest element of each column in integer matrix.

Enter size of integer matrix:
4
Enter Elements in matrix:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Elements in matrix:
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
The Highest value of Column 1 is=13
The Highest value of Column 2 is=14
The Highest value of Column 3 is=15
The Highest value of Column 4 is=16