quotient of a vector space

[[concept]]

Quotient

Let $W\subseteq V$ be a subspace. We define an equivalence relation on $V$ by $v\sim v^{\prime }⟺v-v^{\prime }\in W$ Define $[v]=\{v^{\prime }\in V:v^{\prime }\sim v\}$ the equivalence class of $v$. Then $V|W=\{[v]:v\in V\}$ is called the quotient space which we typically call ”$V$ mod $W$” and notate as $[v]=v+W$ $V|W$ is a vector space such that for all $v_1,v_2\in V$ and $\lambda \in \mathbb{K}$

1. $(v_1+W)+(v_2+W):=(v_1+v_2)+W$
2. $\lambda (v+W)=\lambda v+W$

NOTE

$W=0+W=w+W\forall w\in W$

Mentions

Mentions

TABLE file.mday as "Last Modified"
FROM [[]]
 
FLATTEN choice(contains(artist, this.file.link), 1, "") + choice(contains(author, this.file.link), 1, "") + choice(contains(director, this.file.link), 1, "") + choice(contains(source, this.file.link), 1, "") as direct_source
 
WHERE !direct_source
SORT file.mday ASC
SORT file.name ASC

const { dateTime } = await cJS()
 
return function View() {
	const file = dc.useCurrentFile();
	return <p class="dv-modified">Created {dateTime.getCreated(file)}     ֍     Last Modified {dateTime.getLastMod(file)}</p>
}