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**Diagonal Matrix in C and C++ Language with Examples:**

In this article, I am going to discuss **Diagonal Matrix in C and C++ Language** with Examples. Please read our previous article, where we give a brief **Introduction to Matrices**.

**Diagonal Matrix:**

The following is a diagonal matrix. We have taken a diagonal matrix of order 5×5. That is 5 rows and 5 columns. Here we can see that most of the numbers are ‘0’ and only the elements in the diagonal are non-zero. The important thing is other than diagonal all elements must be ‘0’. Then only we say it is a diagonal matrix.

If we have non-zero elements other than diagonal then that will not be a diagonal matrix. Below is not a diagonal matrix.

The important condition is all the elements other than diagonal must be ‘0’. Let us see how we can define this. For Diagonal Matrix, the condition is:

If row number and column number are the same then the value will be non-zero and if row number and column number are different then the value will be ‘**0**’ in the diagonal matrix.

Now if we have to represent a diagonal matrix in a program then for a matrix, we have to take a two-dimensional array. But if we take a two-dimensional array of size **5×5**, then most of the elements will be zeros.

If we take a two-dimensional array for storing this matrix then most of the elements are zeros and if these are integers an integer is taking 2 bytes, then total how many bytes of memory this array is consuming. There are **5×5** elements that is **25** elements are there and each element is taking **2** bytes. Then it will take **50** bytes of memory.

If we are storing this matrix in **50** bytes of memory then storage of ‘**0**’ elements is unnecessary. It is wasting space as well as when we’ll processing on a diagonal matrix-like if we are adding 2 diagonal matrices then adding ‘**0**’ is of no use or if we are multiplying 2 diagonal matrices then multiplication with zeros is of no use. So, we will be wasting time in the processing of ‘**0**’. So, the idea here is that we want to store only non-zero elements so how we can store only non-zero elements?

For storing non-zero elements we can take just a single dimension array and store these elements. Now let us see how we can represent a diagonal matrix and adjust it in a single dimension array.

We would take a single dimension array size **5** because we have only **5** non-zero elements This study starting index is 0 but here if you observe I have taken then this is from 1 onwards. We will take all the indices starting from 0 onwards to represent a matrix. So let us store the non-zero elements in the array as:

Here we have stored only non-zero elements. Now let us see how we can access these elements from a single dimension array if we want to access them

- If we want to access
**M [0, 0**], this element is present on the**0**index in the array.^{th} - If we want to access
**M [1, 1**], this element is present on the**1**index in the array.

We have stored only non-zero elements in the array. If (i == j) in the matrix, then we can get that element from the array which will index at **M [i]** or **M [j].** Here, ‘**i**’ represents the number of rows in the matrix and ‘**j**’ represents the number of columns in the matrix. Now we will see how we can write a C or C++ program code for representing the diagonal matrix. Let see the code part.

**Diagonal Matrix Code in C Language:**

#include <stdio.h> struct Matrix { int B[10]; int n; }; void Set (struct Matrix *m, int i, int j, int y) { if (i == j) m->B[i - 1] = y; } int Get (struct Matrix m, int i, int j) { if (i == j) return m.B[i - 1]; else return 0; } void Display (struct Matrix m) { int i, j; printf ("Matrix is: \n"); for (i = 0; i < m.n; i++) { for (j = 0; j < m.n; j++) { if (i == j) printf ("%d ", m.B[i]); else printf ("0 "); } printf ("\n"); } } int main () { struct Matrix M; M.n = 5; Set (&M, 1, 1, 2); Set (&M, 2, 2, 5); Set (&M, 3, 3, 8); Set (&M, 4, 4, 3); Set (&M, 5, 5, 7); Display (M); return 0; }

**Output:**

**Diagonal Matrix Code in C++ Language:**

#include <iostream> using namespace std; class DiagonalMatrix { private: int *B; int n; public: DiagonalMatrix () { n = 2; B = new int[2]; } DiagonalMatrix (int n) { this->n = n; B = new int[n]; } ~DiagonalMatrix () { delete[]B; } int GetDimension () { return n; } void Set (int i, int j, int y); int Get (int i, int j); void Display (); }; void DiagonalMatrix::Set (int i, int j, int y) { if (i == j) B[i - 1] = y; } int DiagonalMatrix::Get (int i, int j) { if (i == j) return B[i - 1]; return 0; } void DiagonalMatrix::Display () { cout << "\nMatrix is: " << endl; for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { if (i == j) cout << B[i - 1] << " "; else cout << "0 "; } cout << endl; } } int main () { int d; cout << "Enter Dimensions: "; cin >> d; DiagonalMatrix dm (d); int x; cout << "Enter All Elements: " << endl; for (int i = 1; i <= d; i++) { for (int j = 1; j <= d; j++) { cin >> x; dm.Set (i, j, x); } } dm.Display (); return 0; }

**Output:**

In the next article, I am going to discuss **Lower Triangular Matrix Row-Major Mapping in C and C++ Language** with Examples. Here, in this article, I try to explain **Diagonal Matrix in C and C++ Language** with Examples and I hope you enjoy this Diagonal Matrix in C and C++ Language with Examples article.