Definition: vector space hyperplane (Q2146)
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Definition: vector space hyperplane |
No description defined |
Statements
P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\, |\\, \\vec p,\\vec v_i \\in V,k < \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\} \\\\
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Then:\n\nP is a hyperplane of dimension $k$ in $V \\iff \\{\\vec v_i\\}$ is [[linearly independent#vectors|linearly independent]]
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