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?
 A: Often, the relation $A \succ B$ is used to indicate "$A - B$" is positive definite.
My guess is that $A \succ 7.3$ means $A \succ 7.3 I$; that is, "$A$ is symmetric, and its eigenvalues are strictly greater than $7.3$."
A: 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
A: $% Preamble
  \newcommand{\C}{\mathbb{C}}
  \DeclareMathOperator{\det}{det}
$
One wrote in the answer's comments, a link What's the meaning of $\succ$ operator? might be helpful. Simply, the $\succ$ sign is an analogue of classic $>$ for the non-classic cases. You and everyone other may read it ($\succ$) as $>$ simply, and it is used, or may be used, e.g. at:

*

*As noted in The answer to the respective question, $A\succ B$ may mean, depending on accepted designations, that $−$ is positive definite.

*When $a, b\in\C$ then $a\succ b$ may denote the fact that $|a|>|b|$, where $|\cdot|$ is a classic euclidian norm, i.e. here $|x+\imath y|=\sqrt{x^2+y^2}$. Actually, this example may be transposed for similar other kind of spaces.

*If $a\succ b$ for matrixes, then $\det a>\det b$. Why not.

Generally, it is a relation with the typical $a\succ b, b\succ c\Rightarrow a\succ c$, and with "may not held $a\succeq a$" any $a$ from set, e.g. Even read the Wikipedia if want an exact and long with abstractive examples definition. Good luck
