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Results tagged with linear-algebra
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user 129960
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
2
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1
answer
98
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Existence of a hyperplane with strictly positive coefficients to contain an antichain in $\m...
Given a hyperplane $\alpha^T x = \beta$ in $\mathbb R^n$, with $\beta > 0, \alpha_i > 0$ for all $i \in [n]$. Then for any $\{v^i\} \subseteq \{x \in \mathbb Z^n_+ \mid \alpha^T x = \beta\}$, it's obv …
- 37
1
vote
1
answer
143
views
Rational linear subspace corresponding to an irrational vector
Given a vector $v = (v_1, \ldots, v_n) \in \mathbb{R}^n$, we can associate a rational linear subspace with this vector: assume $\{1, v_i \text{ for }i \in I\}$ is a linear basis of $\{1, v_1, \ldots, …
- 37
0
votes
1
answer
153
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Generalization of Dickson's Lemma
Given $\{v^i\}_{i \in \mathbb{N}} \subseteq \mathbb{N}^n$, and $\cup_{k=1, \ldots, m} C_j = \mathbb{N}^n$ for some $m$, where each $C_k$ is a cone generated by rational vectors. My question is: does t …
- 37