# On the definition of symmetric matrices

by shakgoku
Tags: inner product, matrices, symmetric
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,691 On the definition of symmetric matrices For example, the matrix $$\begin{bmatrix}1+ i & 2- 2i \\ 2- 2i & 3i\end{bmatrix}$$ is "symmetric" but does not have the properties a real symmetric matrix would have (real eigenvalues and a complete set of eigenvectors for example). A Hermitian matrix $$\begin{bmatrix}1+ i & 2- 2i \\ 2+ 2i & 3i\end{bmatrix}$$ will have a complete set of eigenvectors.