Theorem: An $n \times n$ matrix $A$ is nonsingular iff $T(x) = Ax$ is one-to-one (injective). $T$ is injective iff $\ker(T) = \{0\}$, which means $Ax = 0$ has only the trivial solution.
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.