vector subspace (math snippet) (Q2002): Difference between revisions
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Added content item: vector subspace generated by U (math snippet) |
Updated the item for vector subspace (math snippet) from Special:Update |
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| label / en | label / en | ||
vector subspace | vector subspace (math snippet) | ||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
| Property / LaTeX source | |||
| Property / LaTeX source: \\operatorname{span}\\{u_1,\\dots,u_n\\}\n=\n\\left\\{\n\\sum_{i=1}^n \\lambda_i u_i\n\\;\\middle|\\;\n\\lambda_i \\in \\mathbb{K}\n\\right\\} / rank | |||
| Property / note | |||
| Property / note: for $U=\\{u_1,\\cdots, u_n\\} \\in V$. / rank | |||
| Property / attributed to | |||
| Property / attributed to: Rong Martin-Siebler ZHOU / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
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\\} | |||
| Property / LaTeX source: 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\\} / rank | |||
Normal rank | |||
| Property / note | |||
for $\\vec u_1,\\cdots, \\vec u_n \\in V$.\n\nThen Set $U$ is a vector subspace of $V$.\n\nSet $\\{u_1,\\dots,u_n\\}$ is then known as a '''generating set''' of $U$ | |||
| Property / note: for $\\vec u_1,\\cdots, \\vec u_n \\in V$.\n\nThen Set $U$ is a vector subspace of $V$.\n\nSet $\\{u_1,\\dots,u_n\\}$ is then known as a '''generating set''' of $U$ / rank | |||
Normal rank | |||
| Property / attributed to | |||
| Property / attributed to: Rong Martin-Siebler ZHOU / rank | |||
Normal rank | |||
Latest revision as of 07:19, 12 October 2026
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | vector subspace (math snippet) |
No description defined |
Statements
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\\}
0 references
for $\\vec u_1,\\cdots, \\vec u_n \\in V$.\n\nThen Set $U$ is a vector subspace of $V$.\n\nSet $\\{u_1,\\dots,u_n\\}$ is then known as a '''generating set''' of $U$
0 references