Fact. A symmetric matrix $A$ is always square (i.e., $n \times n$).
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 $m = n$.
This distinguishes symmetric matrices from rectangular matrices, for which the notion of symmetry (equality with transpose) is not defined.
Parents
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.