The meaning of symbols related to positive definite matrices

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I have encountered two undefined symbols when reading this paper:

Given two real and positive semidefinite matrices $A$ and $B$ with the same size,

  1. the first relation is written as $$A \npreceq B, $$ which appears on the top of Page $10$.

Does it mean that $(B-A)$ is not positive semidefinite, i.e., the minimal eigenvalue of $(B-A)$ is negative?

  1. another relation is written as $$ A \succsim B ,$$ which appears on the top of Page 9, in the text after equation (2.8).

Is this symbol somehow related to matrix similarity?

Could you help me find a reference where these symbols are clearly defined?