spectral mapping property

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at DataviewInlineApi.eval (plugin:dataview:19027:21)
at evalInContext (plugin:dataview:19028:7)
at asyncEvalInContext (plugin:dataview:19038:32)
at DataviewJSRenderer.render (plugin:dataview:19064:19)
at DataviewJSRenderer.onload (plugin:dataview:18606:14)
at DataviewJSRenderer.load (app://obsidian.md/app.js:1:1182416)
at DataviewApi.executeJs (plugin:dataview:19607:18)
at DataviewCompiler.eval (plugin:digitalgarden:10763:23)
at Generator.next (<anonymous>)
at eval (plugin:digitalgarden:90:61)

Spectral Mapping Property

Let $S^{d \times d}$ be the space of symmetric $d \times d$ matrices. For all $Q \in S^{d \times d}$ , recall that we may write $Q = U^{⊺} Λ U$ , the eigendecomposition. A mapping $f : S^{d \times d} \to S^{d \times d}$ has the spectral mapping property if

Q \mapsto f (Q) := U^{⊺} diag (f (λ_{1} (Q)), \dots, f (λ_{d} (Q))) U

ie, if the eigenvalues of are the eigenvalues of transformed by $f$ .

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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 { 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> }

References

See Also

Mentions