← Mathematical compendium

Published equation contexts

Λ†(Ic)=If\Lambda^\dagger(I_c) = I_f

Why this formula appears here

Λ†\Lambda^\dagger is positive because Λ\Lambda is completely positive and every Λ(ρ)\Lambda(\rho) with ρ\rho ≥\ge 0 is itself a valid state; it is unital, Λ†(Ic)\Lambda^\dagger(I_c) = IfI_f , because Λ\Lambda preserves trace for every input. This duality is the same construction Stinespring used to show that any completely positive map admits a dilation to a larger, unitary description [ 9 ] , and it lets a coarse Hamiltonian be pulled back onto the fine space without the fine space’s own structure ever being disturbed.

Read the full article-specific guide →

Read the representative guide

IcI_c

Symbol I_c

IcI_c is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Read this term in its guide →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

Λ†(Ic)=If\Lambda^\dagger(I_c) = I_f

Equation 19 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Λ†\Lambda^\dagger is positive because Λ\Lambda is completely positive and every Λ(ρ)\Lambda(\rho) with ρ\rho ≥\ge 0 is itself a valid state; it is unital, Λ†(Ic)\Lambda^\dagger(I_c) = IfI_f , because Λ\Lambda preserves trace for every input. This duality is the same construction Stinespring used to show that any completely positive map admits a dilation to a larger, unitary description [ 9 ] , and it lets a coarse Hamiltonian be pulled back onto the fine space without the fine space’s own structure ever being disturbed.

Meanings in this article

Equation guide → · Article →