{"type":"rich","version":"1.0","title":"Definition: vector space hyperplane","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"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\\}, \\\\\">P=\\left\\{ \\vec p + \\sum_{i=1}^{k} \\lambda_{i}\\vec v_{i}\\,  |\\, \\vec p,\\vec v_i \\in V,k &lt; \\dim(V), \\lambda_{i} \\in \\mathbb{F} \\right\\}, \\\\</span><div class=\"wb-embed-note\"><p>and $\\{\\vec v_i\\}$ is <a href=\"/wiki/Linearly_independent#vectors\" title=\"Linearly independent\">linearly independent</a>,\n</p><p>Then $P$ is a hyperplane of dimension $k$ in $V$\n</p></div><footer><cite class=\"wb-embed-author\">Rong Martin-Siebler ZHOU</cite></footer>","width":640,"height":320}