TITLE: What are the $\succ$ and $\prec$ operators for when used with matrices?
QUESTION [8 upvotes]: 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?

REPLY [6 votes]: 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 $7.3$."