Check 3x3 or above matrix is positive semidefinite

Question

I did read the solution to check 2x2 matrix is positive semidefinite: Checking if a matrix is positive semidefinite

Is there other method to check 3x3 or NxN matrix is positive semidefinite?

Answer 1

Use Sylvester's criterion for Positive-Definite Matrices, and analogous theorem for Positive-Semidefinite Matrices.

https://en.wikipedia.org/wiki/Sylvester%27s_criterion