How do you write a c program to determine if a matrix is symmetric or not?

Answer 1

A matrix is symmetric when it is a perfect square and the transpose of the matrix is equal to the original matrix. The implementation is reasonably straightforward and can be done without actually creating the transposed matrix. We simply imagine a dividing line through the main diagonal (top-left to bottom right) and compare the corresponding elements on each side of that diagonal.

bool is_symmetric (int* a, int rows, int cols) {

if (rows!=cols) return false;

for (int row=0, row

for (int col=row+1; col

if (a[row][col] != a[col][row]) return false;

return true;

}

This works because for every element a[row][col] in a square matrix, the corresponding element on the other side of the main diagonal must be a[col][row]. In other words, we simply transpose the subscripts (hence it is called the transpose).

Consider a 4x4 matrix of hexadecimal values:

0 1 2 3

4 5 6 7

8 9 A B

C D E F

The main diagonal line is identified as elements {0, 5, A, F}. Element {7} lies above this line and it corresponds with element {D} below the line. Element {7} is identified with the subscript [1][3] while element {D} is identified with the subscript [3][1].

Note that the inner loop which traverses the columns always starts at col=row+1. This ensures that we always start with the first element after the diagonal element in the current row, and traverse through the remaining elements of that row. In other words, elements in [row][col] are always in the upper-right of the matrix, above the main diagonal. Meanwhile, the corresponding transpose, element [col][row], lies in the lower-left of the matrix, below the main diagonal. There is no need to test the entire array, traversing every column of every row, because there's no point in testing elements on the diagonal itself (we'd be comparing each element to itself and its given that an element is always equal to itself), and there's no point in comparing the lower-left elements to the upper-right elements when we've already performed the reverse comparison. After all, if X==Y then it follows that Y==X because equality is a transitive operation (the result is the same regardless of which side of the operator we place the operands).

Note that in order to replace a square matrix with its transpose, we simply swap the corresponding elements unless the matrix is symmetrical (because, by definition, a symmetrical matrix is equal to its own transpose):

void transpose (int* a, int rows, int cols) {

if (rows!=cols is_symmetric (a, rows, cols)) return;

for (int row=0, row

for (int col=row+1; col

swap (&a[row][col], &a[col][row]);

}