A **symmetric matrix** is a matrix that is equal to its transpose:

$$ A\text{ is symmetric} \Leftrightarrow A = A^T $$

In index notation, we can write this simply as $A_{ij} = A_{ji}$.

A **symmetric matrix** is a matrix that is equal to its transpose:

$$ A\text{ is symmetric} \Leftrightarrow A = A^T $$

In index notation, we can write this simply as $A_{ij} = A_{ji}$.

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