vector space base definition (Q2144)
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | vector space base 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\\}
0 references
And $\\vec u_1,\\dots,\\vec u_n$ are [[linearly independent]],\n\nThen $B=\\{\\vec u_1,\\dots,\\vec u_n\\}$ is a base of $V$
0 references