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37 views

simple intersection understanding problem

I am reading theoretical computer science subject and came across this small step. in the textbook, they defined two contextfree languages: $L_1 = \{ a^i b^j c^j | i,j>0\}$ and $L_2 = \{a^i b^i ...
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147 views

Linear Algebra problem: intersection of a subspace with a cone.

In $\mathbb{R}^n$, consider the closed cone $$C^+ = \{ (x_1, \ldots, x_n) : x_i \geq 0,~~i= 1, \ldots, n\}.$$ Let $S \subseteq \mathbb{R}^n$ be a subspace (of any dimension) such that $S \cap C^+ = ...