Matrix congruence can be seen as the change of basis of a bilinear form Updated 2025-04-24 +Created 1970-01-01
From effect of a change of basis on the matrix of a bilinear form, remember that a change of basis modifies the matrix representation of a bilinear form as:
So, by taking , we understand that two matrices being congruent means that they can both correspond to the same bilinear form in different bases.
visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) is a good quick visual non-mathematical introduction is to it.
One of the Millennium Prize Problems and Hilbert's problems.
What is the Riemann hypothesis REALLY about? by HexagonVideos (2022)
Source. SGML predecessor.
Subset generators:
- github.com/mf1024/ImageNet-datasets-downloader generates on download, very good. As per github.com/mf1024/ImageNet-Datasets-Downloader/issues/14 counts go over the limit due to bad multithreading. Also unfortunately it does not start with a subset of 1k.
- github.com/BenediktAlkin/ImageNetSubsetGenerator
Unfortunately, since ImageNet is a closed standard no one can upload such pre-made subsets, forcing everybody to download the full dataset, in ImageNet1k, which is huge!
Implosion-type fission weapons are more complicated than gun-type fission weapon because you have to precisely coordinate the detonation of a bunch of explosives.
Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.
And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!
Bibliography:
- www.youtube.com/watch?v=EK_6OzZAh5k How Electron Spin Makes Matter Possible by PBS Space Time (2021)
The scale where human brain simulation becomes possible according to some estimates.
OMG, the second half of the game where the world becomes quite open and all backstories are revealed, is one of the best gaming moments ever.
Generalization of orthogonal group to preserve different bilinear forms. Important because the Lorentz group is .
There are unlisted articles, also show them or only show them.