If $A\in M_{n}(\mathbb{F})$,where $\mathbb{F}=\mathbb{R}$ or $\mathbb{F}=\mathbb{C}$
and $A$ satisfy: $A'=A$ (where $A'$ is the transposed matrix of $A$).we say:
$A$ is a symmetric matrix
ok, If $A=\begin{bmatrix}a_{11}& ... & a_{1n}\\ ... & ... & ...\\ a_{n1}& ... & a_{nn}\end{bmatrix}.$
we denote the principal minor of $A$ of order $r$ by $det\begin{bmatrix}a_{i_{1}i_{1}}& ... & a_{i_{1}i_{r}}\\ ... & ... & ...\\ a_{i_{r}i_{1}}& ... & a_{i_{r}i_{r}}\end{bmatrix}.$
where $1\leq i_{1}< ... < i_{r}\leq n$
and my question is: If $A$ is a symmetric matrix or a Hermite Matrix, then $A$ has a nonzero principal minor which order equal $rank(A)$