16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 9.3.6

Operators on Inner Product Spaces

Mathematics — Linear Algebra · positive-matrices

Problem

Which of the following matrices are positive?

\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \qquad \begin{bmatrix} 1 & 1+i \\ 1-i & 3 \end{bmatrix}, \qquad \begin{bmatrix} 1 & -1 & 1 \\ 2 & -1 & 1 \\ 3 & -1 & 1 \end{bmatrix}, \qquad \begin{bmatrix} 1 & \frac{1}{2} & \frac{1}{3} \\ \frac{1}{2} & \frac{1}{3} & \frac{1}{4} \\ \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \end{bmatrix}.