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)

another question is: the Geometric meaning of Symmetric matrix is?