{"type":"rich","version":"1.0","title":"vector subspace (math snippet)","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"U=\\operatorname{span}\\{\\vec u_1,\\dots,\\vec u_n\\}\n=\\left\\{\n\\sum_{i=1}^n \\lambda_i \\vec u_i\n\\;\\middle|\\;\n\\lambda_i \\in \\mathbb{F}\n\\right\\}\">U=\\operatorname{span}\\{\\vec u_1,\\dots,\\vec u_n\\}\n=\\left\\{\n\\sum_{i=1}^n \\lambda_i \\vec u_i\n\\;\\middle|\\;\n\\lambda_i \\in \\mathbb{F}\n\\right\\}</span><div class=\"wb-embed-note\"><p>for $\\vec u_1,\\cdots, \\vec u_n \\in V$.\n</p><p>Then Set $U$ is a vector subspace of $V$.\n</p><p>Set $\\{u_1,\\dots,u_n\\}$ is then known as a <b>generating set</b> of $U$\n</p></div><footer><cite class=\"wb-embed-author\">Rong Martin-Siebler ZHOU</cite></footer>","width":640,"height":320}