# Thread: Properties of real symmetric matrices

1. ## Properties of real symmetric matrices

Hello Everyone, what are properties of real symmetric nxn matrices other than
(1) $A \in M_{n \times \n}\Rightarrow A = A^t$
(2) $\text{dim}M_{n\times n} = \frac{n(n+1)}{2}$

I can't think of any others...
A little help would be appreciated

2. The eigenvalues are real, and the eigenvectors are an orthonormal basis. In fact, it is diagonalizable.