I have a square symmetric matrix. I want to check if it is positive definite. I understand that according to wikipedia if all the eigenvalues are positive, the matrix is positive definite. I don't know if this means $\lambda$>0 or if it means $\lambda \geq$0. Because I have $\lambda$=0.
According to wiki zero isn't positive or negative. I am just a little confused on this topic.
Best Answer
A Positive Definite has full rank: all its eigenvalues are strictly positive.
A square symmetric matrix with non-negative eigenvalues (i.e., eigenvalues that are positive or zero) is called Positive Semi-Definite (PSD).