What are the $\succ$ and $\prec$ operators for when used with matrices? I understand that $A\succ0$ means that "A is a positive definite matrix" (i.e.; all of the eigenvalues of A are positive).
But what does it mean when the right hand side is a different value than zero? For example, what does the expression below imply?
$$ A \succ 7.3 $$
Also, what is the name of this operator?

Unfortunately I cannot answer your question completely. But I can answer the last one. The name of this operator is succeed. You can see all names of this math operator and its relation from this latex code, given below:
http://www.access2science.com/latex/Binary.html
