I'm studying a book and encountered with that: the set of positive definite matrices are the interior of set of positive semidefinite matrices.
What is the norm here?
2026-02-22 21:32:09.1771795929
set of positive definite matrices are the interior of set of positive semidefinite matrices
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One can take the Frobenius norm $$ ||A||^2=\langle A,A\rangle=Tr(AA^T), $$ see the article Properties of positive (semi)definite matrices. Example $B5$ is the statement you have mentioned, on page $239$.