# Symmetric matrices are square.

Put content here**Fact.** A symmetric matrix $A$ is always *square* (i.e., $n \times n$).
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**Reason:** For $A = A^T$ to hold, $A$ must have the same number of rows and columns. If $A$ is $m \times n$, then $A^T$ is $n \times m$, so equality requires $m = n$.
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This distinguishes symmetric matrices from rectangular matrices, for which the notion of symmetry (equality with transpose) is not defined.

# Parents

* Symmetric matrices