inner product

[[concept]]

Topics

const fieldName = "theme"; // Your field with links
const oldPrefix = "Thoughts/01 Themes/";
const newPrefix = "Digital Garden/Topics/";
 
const relatedLinks = dv.current()[fieldName];
 
if (Array.isArray(relatedLinks)) {
    // Map over the links, replace the path, and output only clickable links
    dv.el("span",
        relatedLinks
            .map(link => {
                if (link && link.path) {
                    let newPath = link.path.startsWith(oldPrefix)
                        ? link.path.replace(oldPrefix, newPrefix)
                        : link.path;
                    return dv.fileLink(newPath);
                }
            })
            .filter(Boolean).join(", ") 
	// Remove any undefined/null items
    );
} else {
    dv.el(dv.current().theme);
}
 
 

Inner Product

An inner product on a vector space $V$ over field $K$ is a function $⟨,⟩:V\times V\to K$ such that for all $x,y,z\in V$ and all $c\in K$ we have

1. $⟨x,x⟩$ is real, nonnegative. Also, $⟨x,x⟩=0⟺x=0$

2. $⟨x+y,z⟩=⟨x,z⟩+⟨y,z⟩$

3. $⟨cx,z⟩=c⟨x,z⟩$ (2 and 3 indicate that this is linear)

4. $⟨x,z⟩=\overline{⟨z,x⟩}$ (ie symmetric)

If all of these hold, then $V$ is an inner product space.

${\mathbb{C}}^n$ over $\mathbb{C}$.

• Euclidean inner product: $⟨x,z⟩:=z^{\ast }x$
• some $A\in M_n$ positive definite: $⟨x,z{⟩}_A:=z^{\ast }Ax$ Note that the euclidean inner product is a special case of the second, where $A$ is the identity!

Mentions

Mentions

const modules = await cJS()
 
const COLUMNS = [  
	{ id: "Name", value: page => page.$link },  
	{ id: "Last Modified", value: page => modules.dateTime.getLastMod(page) },
];  
  
return function View() {  
	const current = dc.useCurrentFile();
// Selecting `#game` pages, for example. 
	let queryString = `@page and linksto(${current.$link})`;
	let pages = dc.useQuery(queryString);
	
	// check types
	pages = pages.filter( (p) => !modules.typeCheck.checkAll(p, current) ).sort()
	
	
	return <dc.Table columns={COLUMNS} rows={pages} paging={20}/>;  
}  

const page = dv.current();
 
let earliest;
if (page.created) {
	earliest = moment(dv.current().created.toString()).isBefore(moment(page.file.cday))
	? page.created.toString()
	: page.file.cday;
} else {
	earliest = page.file.cday;
}
 
let latest = (Array.isArray(page.modified) && page.modified.length > 0)
	? page.modified[-1]
	: page.file.mday;
 
dv.el(
	'span',
	"Created " +
		moment(earliest).format("YYYY-MM-DD") + 
		"    ֍     Last Modified " +
		moment(latest).format("YYYY-MM-DD"),
  { cls: "dv-modified" }
);