0
$\begingroup$

This question already has an answer here:

Suppose that $A, B$ are real $n\times n$ symmetric positive definite matrices such that $A - B$ is positive semi-definite. Does it follow that $A^2 - B^2$ is positive semi-definite?

$\endgroup$

marked as duplicate by user1551 matrices Dec 19 '18 at 17:18

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.