Java Program to Find the Determinant of a Matrix (original) (raw)
Last Updated : 01 May, 2025
The **determinant of a matrix is a special calculated value that can only be calculated if the matrix has same number of rows and columns (square matrix). It is helpful in determining the system of linear equations, image processing, and determining whether the matrix is singular or non-singular.
In this article, we are going to learn the step-by-step procedure to calculate the determinant of a matrix and Java implementations using both recursive and non-recursive approaches.
**Procedure to Calculate
- First, we need to calculate the cofactor of all the elements of the matrix in the first row or first column.
- Then, multiply each element of the first row or first column by their respective cofactor.
- At last, we need to add them up with alternate signs.
**Examples:
**Determinant of 2*2 matrix:
[4, 3]
[2, 3]= (4*3)-(3*2)
= 12-6
= 6
**Determinant of 3*3 matrix:
[1, 3, -2]
[-1, 2, 1]
[1, 0, -2]= 1(-4-0)-3(2-1)+(-2)(0-2)
= -4-3+4
= -3
**Note:
- The determinant of **1*1 matrix is the element itself.
- The **Cofactor of any element of the stated matrix can be calculated by eliminating the row and the column of that element from the matrix stated.
Let’s see an example to get a clear concept of the above topic.
Determinant of a Matrix in Java
**Example 1: Finding the determinant of a matrix **using recursion.
Java `
// Java program to find // Determinant of a matrix // using recursion class Geeks {
// Dimension of input square matrix
static final int N = 2;
// Function to get cofactor of
// mat[p][q] in temp[][]. n is
// current dimension of mat[][]
static void getCofactor(int mat[][], int temp[][],
int p, int q, int n)
{
int i = 0, j = 0;
// Looping for each element
// of the matrix
for (int row = 0; row < n; row++) {
for (int col = 0; col < n; col++) {
// Copying into temporary matrix
// only those element which are
// not in given row and column
if (row != p && col != q) {
temp[i][j++] = mat[row][col];
// Row is filled, so increase
// row index and reset col index
if (j == n - 1) {
j = 0;
i++;
}
}
}
}
}
/* Recursive function for finding determinant
of matrix. n is current dimension of mat[][]. */
static int determinantOfMatrix(int mat[][], int n)
{
int D = 0; // Initialize result
// Base case : if matrix
// contains single element
if (n == 1)
return mat[0][0];
// To store cofactors
int temp[][] = new int[N][N];
// To store sign multiplier
int sign = 1;
// Iterate for each element of first row
for (int f = 0; f < n; f++) {
// Getting Cofactor of mat[0][f]
getCofactor(mat, temp, 0, f, n);
D += sign * mat[0][f]
* determinantOfMatrix(temp, n - 1);
// terms are to be added
// with alternate sign
sign = -sign;
}
return D;
}
// function for displaying the matrix
static void display(int mat[][], int row, int col)
{
for (int i = 0; i < row; i++) {
for (int j = 0; j < col; j++)
System.out.print(mat[i][j]);
System.out.print("\n");
}
}
// Driver code
public static void main(String[] args)
{
int mat[][] = { { 4, 3 }, { 2, 3 } };
System.out.print("Determinant "
+ "of the matrix is: "
+ determinantOfMatrix(mat, N));
}}
`
Output
Determinant of the matrix is: 6
**Time complexity: O(n3)
**Example 2: **Non-recursive Implementation of finding determinant of a matrix.
Java `
// Java program to find Determinant of a matrix class Geeks {
// Dimension of input square matrix
static final int N = 4;
// Function to get determinant of matrix
static int determinantOfMatrix(int mat[][], int n)
{
int num1, num2, det = 1, index,
total = 1; // Initialize result
// temporary array for storing row
int[] temp = new int[n + 1];
// loop for traversing the diagonal elements
for (int i = 0; i < n; i++) {
index = i; // initialize the index
// finding the index which has non zero value
while (mat[index][i] == 0 && index < n) {
index++;
}
if (index == n) // if there is non zero element
{
// the determinant of matrix as zero
continue;
}
if (index != i) {
// loop for swapping the diagonal element row
// and index row
for (int j = 0; j < n; j++) {
swap(mat, index, j, i, j);
}
// determinant sign changes when we shift
// rows go through determinant properties
det = (int)(det * Math.pow(-1, index - i));
}
// storing the values of diagonal row elements
for (int j = 0; j < n; j++) {
temp[j] = mat[i][j];
}
// traversing every row below the diagonal
// element
for (int j = i + 1; j < n; j++) {
num1 = temp[i]; // value of diagonal element
num2 = mat[j]
[i]; // value of next row element
// traversing every column of row
// and multiplying to every row
for (int k = 0; k < n; k++) {
// multiplying to make the diagonal
// element and next row element equal
mat[j][k] = (num1 * mat[j][k])
- (num2 * temp[k]);
}
total = total * num1; // Det(kA)=kDet(A);
}
}
// multiplying the diagonal elements to get
// determinant
for (int i = 0; i < n; i++) {
det = det * mat[i][i];
}
return (det / total); // Det(kA)/k=Det(A);
}
static int[][] swap(int[][] arr, int i1, int j1, int i2,
int j2)
{
int temp = arr[i1][j1];
arr[i1][j1] = arr[i2][j2];
arr[i2][j2] = temp;
return arr;
}
// Driver code
public static void main(String[] args)
{
int mat[][] = { { 1, 0, 2, -1 },
{ 3, 0, 0, 5 },
{ 2, 1, 4, -3 },
{ 1, 0, 5, 0 } };
// Function call
System.out.printf(
"Determinant of the matrix is: %d",
determinantOfMatrix(mat, N));
}}
`
Output
Determinant of the matrix is: 30
**Time complexity: O(n3)