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What is an easy way of checking if this matrix on $R^2_{++}$ is positive semidefinite ? I saw this thread Checking if a matrix is positive semidefinite using Sylvester's criterion but don't understand what principal minors are. My class works ONLY on 2x2 matrices and did not mention anything about minors.

For 2x2 matrices, without using the word minors/principals/etc, do I just have to find out if the 3 conditions are satisfied ?

$H[0][0] \ge 0$

$H[1][1] \ge 0$

$H[0][0] \times H[1][1] - H[0][1] \times H[1][0] \ge 0$

H = $$\begin{bmatrix}\frac{2x_2^2}{(x_1x_2)^3} & \frac{1}{(x_1x_2)^2} \\\frac{1}{(x_1x_2)^2} & \frac{2x_1^2}{(x_1x_2)^3}\end{bmatrix}$$

What about positive definite ?

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