Example of hermitian semidefinite positive Could someone show me an example of a $3\times 3$ hermitian semidefinite positive matrix? (I mean not only symmetric, but hermitian, with complex coefficients)

There is a lot of work on hermitian semidefinite positive matrices, but it seems that people talk about them and don't take the time to exhibit examples.
Note that a Hermitian matrix will be positive definite if and only if it has positive eigenvalues.  A good "recipe" to quickly build a positive definite matrix is to select diagonal elements that are sufficiently big, since selecting large positive diagonal entries will guarantee positive eigenvalues (positive, since the eigenvalues of a Hermitian matrix are necessarily real).  An example of a more precise (and useful) description of this phenomenon is given by the Gershgorin circle theorem.

So with that being said: without computing eigenvalues explicitly, I can guarantee that the Hermitian matrix
$$
\pmatrix{100 &amp; 1 - 2i &amp; 3 + 5i\\
1 + 2i &amp; 100 &amp; -9 + i\\
3 - 5i &amp; -9 - i &amp; 100}
$$
is positive definite.
Hint: The identity matrix is Hermitian and psd.