spectral mapping property

[[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)
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                        : link.path;
                    return dv.fileLink(newPath);
                }
            })
            .filter(Boolean).join(", ") 
	// Remove any undefined/null items
    );
} else {
    dv.el(dv.current().theme);
}
 
 

Spectral Mapping Property

Let ${\mathcal{S}}^{d\times d}$ be the space of symmetric $d\times d$ matrices. For all $Q\in {\mathcal{S}}^{d\times d}$, recall that we may write $Q=U^{⊺}\Lambda U$, the eigendecomposition. A mapping $f:{\mathcal{S}}^{d\times d}\to {\mathcal{S}}^{d\times d}$ has the spectral mapping property if $Q\mapsto f(Q):=U^{⊺}\text{diag}(f({\lambda }_1(Q)),\dots ,f({\lambda }_d(Q)))U$ ie, if the eigenvalues of are the eigenvalues of transformed by $f$.

NOTE

ie, such functions apply elementwise to the eigenvalues of $Q$.

Note

Note that these functions are unitarily invariant, ie $f\left(V^{⊺}QV\right)=V^{⊺}f(Q)V$

References

References

See Also

Mentions

Mentions

const modules = await cJS()
 
const COLUMNS = [  
	{ id: "Name", value: page => page.$link },  
	{ id: "Last Modified", value: page => modules.dateTime.getLastMod(page) },
];  
  
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	const current = dc.useCurrentFile();
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	let pages = dc.useQuery(queryString);
	
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}  

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