vector space basis definition (Q2144)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | vector space basis definition |
No description defined |
Statements
\\forall \\vec v \\in V, \\vec v=\\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\\}
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And $\\vec u_1,\\dots,\\vec u_n$ are [[linearly independent]],\n\nThen $B=\\{\\vec u_1,\\dots,\\vec u_n\\}$ is a basis of $V$\n\n$n$ is known as the '''dimension''' of $V$
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