# 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?

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Normally $A > B$ means $A - B$ is positive. Perhaps, when $k$ is a number, $A > k$ actually means $A > kI$, where $I$ is the identity? – Christopher A. Wong Feb 26 '13 at 23:45
It is not an operator. It is a relation. – Willie Wong Feb 27 '13 at 0:14

I also asked meaning of $\succ$ in another question. Might be you want to check it: math.stackexchange.com/questions/644731/… – Suat Atan Jan 21 '14 at 8:15
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 $7.3$."