Hi Mathematics Community!
I am attempting to teach myself linear algebra and have stumbled across a topic that I can't seem to fully grasp and am hoping you can help. I understand positive and negative definite, but I don't understand the concept of (or how to decide) semidefiniteness of a matrix. I believe that you are supposed to take a permutation of the number of the rows in the matrix and then apply that somehow, but that is the extent of my knowledge.
Any help is greatly appreciated! Thank you.
PS. I also read somewhere that there is an eigenvalue method. However, it stated that there was a need for a symmetric matrix. What do I do if there is not a symmetric matrix?
You may use Sylvester's criterion (look e.g. in wiki) for an $n\times n$ matrix $M$: if each determinant of every $k\times k$ principal submatrix of $M$ is non-negative then so is $M$. Here, a $k\times k$ principal submatrix means choosing $k$ entries $I=\{i_1,\ldots, i_k\}$ among the rows and the same entries $I$ among the columns.
The permutations of rows as you mention doesn't quite make sense