第2195题：Positive Definite Matrix

About Positive Definite Matrices, Which of the following sentences is correct?

A. A square matrix is called positive definite if it is symmetric and all its eigenvalues $\lambda$ are positive, that is $\lambda > 0$ .

B. If $A$ is positive definite, then it is invertible and $det(A) \geqslant 0$ .

C. A symmetric matrix $A$ is positive definite if and only if $\bold{x}^T A \bold{x}$ $\geqslant 0$ for every column $\bold{x} \ne \bold{0}$ in $\mathbb{R}^n$ .

D. If $B$ is any invertible $n \times n$ matrix , then $A=B^T B$ is positive definite.