Well, the question is as simple as that: Given a symmetric and positive semidefinite matrix. Is it true that the largest diagonal entry is always smaller or equal to the largest eigenvalue?
I was just getting a little frustrated while proving this for a specific kind of matrix (that happens to be symmetric and positve definite). So I'm wondering whether I can just skip the algebra and show that this is true in general. But a quick web search didn't reveal any promising references.
Can someone clear up for me whether this is true or not?