Waaat? You can find eigenvectors for a hermitian matrix from the eigenvalues of it and its submatrices? New linear algebra fact discovered by physicists researching neutrinos I didn't quite believe it so I tried it myself: It works.
Particle physicists have stumbled across a previously hidden connection between two ubiquitous objects in math.
Almost incredible : ! physicists discover new general relationship between eigenvectors and eigenvalues of the minor ! , Terence Tao checks, and does three different proofs within two hours. 🔥
My take on today's impeachment proceedings
A new discovery about the bedrock of mathematics might also help us gain a better understanding of the most mysterious of fundamental particles: the neutrino.
In an effort to calculate how neutrinos change, three physicists discovered an unexpected relationship between some of the most ubiquitous objects in math.
Attempts to simplify calculations of neutrino oscillations have uncovered "a new insight into centuries-old mathematical objects." reports in :
So [the physicists] took a chance and contacted Tao. “To our surprise, he replied in under two hours saying he’d never seen this before,” Parke said. Tao’s reply also included three independent proofs of the identity.
It’s “too good to be true”, thought mathematician Terence Tao when he opened a letter from three physicists suggesting they had come up with a formula so “short and simple — it should have been in textbooks already”. (via )
Neutrinos Lead to Unexpected Discovery in Basic Math. Three physicists wanted to calculate how neutrinos change. They ended up discovering an unexpected relationship between some of the most ubiquitous objects in math.
I never thought it possible to express eigenvectors by using only eigenvalues. Turns out it is, if you allow using e-values of minors. Only works for Hermitian matrices.
Eigenvectors from Eigenvalues. Neutrinos Lead to Unexpected Discovery in Basic Math via
Neutrinos Lead to Unexpected Discovery in Basic Math via
“Neutrinos Lead to Unexpected Discovery in Basic Math”, at Quanta.
I sometimes joke that I’ll name my 2nd smallest son Eigenvector Momennejad (no one will mess with him on the playground!). Now this article is treating Eigenvector with scary double quotes like it’s alien math 👾 my hypothetical son is offended.