Afham

Liberté, égalité, fidelité

08.05.2025 20:30 — 👍 2    🔁 0    💬 0    📌 0

I realized I did not make clear that the e.vals have to be real and positive. Sorry!

But I did some further numerics and you are right in general. I generated X = AB with A, B >= 0 and used partial trace. X can have complex evals in general.

And yes, it's good to see these kinds of posts here!

23.03.2025 00:16 — 👍 1    🔁 0    💬 0    📌 0

Thanks for the reply! But the example you posted has complex e.vals which are conjugates of each other with +ve real part, hence the trace and det condition will be satisfied without the e.vals being (real) positive.

23.03.2025 00:16 — 👍 1    🔁 0    💬 1    📌 0

Q: Let X be a (non-Hermitian) matrix with positive eigenvalues (such X = AB, where A,B >= 0) and let Λ be a Completely positive map. Is Λ(X) guaranteed to be a matrix with positive eigenvalues?

That is, do CP maps take EVERY (including non-Herm) matrix with pos evals to matrices with pos evals?

21.03.2025 22:09 — 👍 1    🔁 0    💬 1    📌 0

Train your biceps with some dagger curls! Although \ddagger curls would be easier for balance.

18.03.2025 21:10 — 👍 1    🔁 0    💬 0    📌 0

Haha, took it almost verbatim from the Preliminaries of my thesis!

14.03.2025 22:12 — 👍 2    🔁 0    💬 0    📌 0

Here is a 'simple' 3-line proof for this statement!

(Although the simplicity hides behind the form and properties of the matrix geometric mean.)

14.03.2025 17:24 — 👍 15    🔁 2    💬 1    📌 0