What is matrix inequality such as $A>0$ or $A\succ 0$? I am trying to gather here different meanings of the same symbol, inequality symbol or the succ symbol. I find many other use them so many different ways.
Sometimes, $A&gt;0$ means $\bar x^T A \bar x &gt;0$. Sometimes, $A&gt;0$ means element-wise i.e. $a_{i,j}&gt;0$ for all $i,j$.

How do I know which definition of inequality people are meaning?

Examples


[Solved] Meaning of this? Why is it $A\succ 0$?  LMI and example from Boyd's book. $\succ$ means positive-definiteness: check PD with Cholenksy decomposition, positive eigen-value check or Sylvester criteria. Chat.

Strict matrix inequality defined here requiring symmetric matrices.
The curved symbol (in my experience) means that the difference is positive definite (so, with zero it means that the matrix is positive definite). The $&gt;$ depends on the context.
For squared matrix $A$, $A&gt;0$ means that $A$ is positive definite. Also, the real parts of all of $A$s eigenvalues are positive.