graphon shift operators are self-adjoint

[[concept]]

Theorem

Let $W$ be a graphon and $T_{W}$ its graphon shift operator. Then $T_{W}$ is self-adjoint.

Proof

graphons are symmetric. So

⟨ T_{W} x, y ⟩ = ⟨ x, T_{W} y ⟩

Review

#flashcards/math/dsg

graphon shift operators are {self-adjoint} because graphons are {symmetric functions}

Mentions

File
2025-03-31 lecture 16

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>
}