Update: The tag limits-colimits was created by Martin. So it seems that the best course of action is now to merge these two tags, or add them as synonyms. Do we need the direct-limit and inverse-limits? I have no opinion on the matter, but maybe those should be merged into a single tag someho...

I propose creating limits-colimits for limits and colimits in the sense of category theory. (Perhaps it might be useful to create also colimits and categorical-limits and add them as synonyms.) We have many questions about limits and colimits in category-theory tag. Some of them are tagged as li...

Let $H$ be a positive definite matrix and $I$ the identity matrix. If $k_1,k_2>0$, can we conclude that $k_1H-k_2I$ is positive definite if $k_1\gg k_2$?

If matrix $A$ is positive definite, what properties does its vectorization column vector has? vectorization means $vec(A)$, that is to make it into a single column by list first column, then 2nd column, then 3rd.

If $A$ is a positive definite matrix, B is not sure but $tr(B)>0$ where $tr$ is trace, will $tr(AB)>0$ ? that is the trace of the product of those two matrices. B is not a diagonal matrix or more specifically, $B=vec(D)*(c \otimes c)$ where c is any row vector and $D$ is positive definite. $vec$ ...