## 每週問題 January 21, 2013

Give an example of a real matrix all of whose determinants of principal submatrices and eigenvalues are positive, the matrix, however, is not positive definite.

$A=\left[\!\!\begin{array}{cr} 1&-4\\ 0&1 \end{array}\!\!\right]$

$\displaystyle B=\frac{A+A^T}{2}=\left[\!\!\begin{array}{rr} 1&-2\\ -2&1 \end{array}\!\!\right]$

PowSol-Jan-21-13