my question is between mathematics, physics and informatics. Suppose i have an Hamiltonian (hermitian matrix) that i can diagonalize. The matrix that allows this transformation is a unitary matrix build with the eigenvectors of my Hamiltonian.
Now suppose I select only the $n$ first eigenvectors of length $m$. The matrix $A$ can be build with those eigenvectors, it's size is $m\times n$ with $m>n$. The eigenvectors are the column of the $A$ matrix. The $n$ eigenvectors are of course linearly independent.
Then, I select $n$ rows of my $A$ matrix and build $B$, a new $n\times n$ matrix. It is logic that $B$ can be such that $\det(B)=0$.
Here is my question : Is there a way (using Lapack if possible) to select randomly the rows in order to be sure that $\det(B)\neq0$ ?