# Properties of real symmetric matrices

• August 7th 2010, 12:26 AM
rebghb
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
• August 7th 2010, 03:27 AM
Ackbeet
The eigenvalues are real, and the eigenvectors are an orthonormal basis. In fact, it is diagonalizable.