If a matrix is symmetric, what can be said about its elements? (2021)

If a matrix is symmetric, what can be said about its elements? (2021)

Step 1: Understand what a matrix is. A matrix is a rectangular array of numbers arranged in rows and columns.
Step 2: Learn what a symmetric matrix is. A symmetric matrix is a square matrix that is equal to its transpose.
Step 3: Know what transpose means. The transpose of a matrix is formed by flipping it over its diagonal, which means rows become columns and columns become rows.
Step 4: Identify the condition for symmetry. For a matrix to be symmetric, the element in the ith row and jth column (Aij) must be equal to the element in the jth row and ith column (Aji).
Step 5: Apply the condition. This means that if you look at any element in the matrix, it should be the same as its corresponding element on the opposite side of the diagonal.

Symmetric Matrix – A matrix that is equal to its transpose, meaning the elements across the main diagonal are mirrored.