게으른맽랩 lazy matlab

Thm. Every vector space has a basis. (even in the case of infinite dimension)  proof) Let $V$ be a vector space other than $\{0\}$. Pick a vector $x \neq 0$ from $V$. Consider the set $X = \{S \subseteq V | x \in S, S$ is linearly independent$\}.$ Then $(X, \subseteq)$ is an ordered set. Obviously $X$ is nonempty because $\{x\}\in X$. By Hausdorff maximal principle (see below), $X$ has a maximal..