JavaScript Program to Check if a Matrix is Symmetric

A symmetric matrix is a square matrix that equals its transpose, meaning element at position (i,j) equals element at position (j,i). In mathematical terms, A = A^T, where A is the matrix and A^T is its transpose.

In this article, we'll explore JavaScript programs to check if a given matrix is symmetric using different approaches.

Example Input and Output

Input:
matrix = [[1, 2, 3], [2, 4, 5], [3, 5, 6]]

Output:
The matrix is symmetric: true

Input:
matrix = [[1, 2, 3], [2, 4, 5], [3, 9, 6]]

Output:
The matrix is symmetric: false

Using Transpose Matrix Comparison

This approach creates the transpose of the given matrix and compares it element by element with the original matrix.

function getTranspose(matrix) {
    const rows = matrix.length;
    const cols = matrix[0].length;
    
    // Check if matrix is square
    if (rows !== cols) {
        return null;
    }
    
    const transpose = [];
    for (let i = 0; i 

Matrix: [ [ 1, 2, 3 ], [ 2, 4, 5 ], [ 3, 5, 6 ] ]
Is symmetric: true
Matrix: [ [ 1, 2, 3 ], [ 2, 4, 5 ], [ 3, 9, 6 ] ]
Is symmetric: false


Using Direct Element Comparison

This optimized approach directly compares matrix[i][j] with matrix[j][i] without creating a transpose matrix, using less memory.

function isSymmetricDirect(matrix) {
    const rows = matrix.length;
    const cols = matrix[0].length;
    
    // Must be a square matrix
    if (rows !== cols) {
        return false;
    }
    
    // Compare only upper triangle with lower triangle
    for (let i = 0; i  {
    console.log(`Test ${index + 1}:`, matrix);
    console.log(`Is symmetric: ${isSymmetricDirect(matrix)}`);
    console.log('---');
});


Test 1: [ [ 1, 2, 3 ], [ 2, 4, 5 ], [ 3, 5, 6 ] ]
Is symmetric: true
---
Test 2: [ [ 1, 2 ], [ 2, 1 ] ]
Is symmetric: true
---
Test 3: [ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
Is symmetric: false
---
Test 4: [ [ 5 ] ]
Is symmetric: true
---


Complexity Comparison

Key Points

• A matrix must be square (rows = columns) to be symmetric
• Only need to check upper or lower triangle due to symmetry
• Direct comparison is more memory efficient than transpose approach
• Single-element matrices are always symmetric

Conclusion

The direct comparison method is more efficient as it uses constant space complexity and avoids creating a transpose matrix. Both approaches have the same time complexity but the direct method is the preferred solution for checking matrix symmetry in JavaScript.