Calendar Updated +Created
Electric potential Updated +Created
End-to-end encryption Updated +Created
Inflation (cosmology) Updated +Created
Lepton Updated +Created
Can be contrasted with baryons as mentioned at baryon vs meson vs lepton.
Slang Updated +Created
Open source EDA tool Updated +Created
Merkle tree Updated +Created
Paul Allen Updated +Created
PCI Updated +Created
Video 1.
PCIe computer explained by ExplainingComputers (2018)
Source.
Personal computer Updated +Created
Personalized learning Updated +Created
Inferior compared to self-directed learning, but better than the traditional "everyone gets the same" approach.
Video 1.
Project SOCRATES at Illinois University Urban-Champaign (1966)
Source. It is 2020, and we are not there yet. God!
Phase shift gate Updated +Created
Phi Updated +Created
Two lower case variants... both used in mathematical notation, and for some reason, in LaTeX \varphi is the one that actually looks like the default standard modern lowercase phi, while \phi is the weird one. I love life.
Sylvain Poirier Updated +Created
Ciro Santilli feels a bit like this guy:
singlesunion.org/ so cute, he's looking for true love!!! This is something Ciro often thinks about: why it is so difficult to find love without looking people in the eye. The same applies to jobs to some extent. He has an Incel wiki page: incels.wiki/w/Sylvain_Poirier :-)
Figure 1.
Sylvain's photo from his homepage.
Source. He's not ugly at all! Just a regular good looking French dude.
Video 1.
Why learn Physics by yourself by Sylvain Poirier (2013)
Source.
Physics journal Updated +Created
The strongest are:
Sylvester's law of inertia Updated +Created
The theorem states that the number of 0, 1 and -1 in the metric signature is the same for two symmetric matrices that are congruent matrices.
For example, consider:
The eigenvalues of are and , and the associated eigenvectors are:
symPy code:
A = Matrix([[2, sqrt(2)], [sqrt(2), 3]])
A.eigenvects()
and from the eigendecomposition of a real symmetric matrix we know that:
Now, instead of , we could use , where is an arbitrary diagonal matrix of type:
With this, would reach a new matrix :
Therefore, with this congruence, we are able to multiply the eigenvalues of by any positive number and . Since we are multiplying by two arbitrary positive numbers, we cannot change the signs of the original eigenvalues, and so the metric signature is maintained, but respecting that any value can be reached.
Note that the matrix congruence relation looks a bit like the eigendecomposition of a matrix:
but note that does not have to contain eigenvalues, unlike the eigendecomposition of a matrix. This is because here is not fixed to having eigenvectors in its columns.
But because the matrix is symmetric however, we could always choose to actually diagonalize as mentioned at eigendecomposition of a real symmetric matrix. Therefore, the metric signature can be seen directly from eigenvalues.
Also, because is a diagonal matrix, and thus symmetric, it must be that:
What this does represent, is a general change of basis that maintains the matrix a symmetric matrix.
Symbolic artificial intelligence Updated +Created
Obsidian (software) Updated +Created
Good:
Bad:
Figure 1.
Obsidian demo
. Source.
Synthetic geometry of the real projective plane Updated +Created
It good to think about how Euclid's postulates look like in the real projective plane:
Unlike the real projective line which is homotopic to the circle, the real projective plane is not homotopic to the sphere.
The topological difference bewteen the sphere and the real projective space is that for the sphere all those points in the x-y circle are identified to a single point.
One more generalized argument of this is the classification of closed surfaces, in which the real projective plane is a sphere with a hole cut and one Möbius strip glued in.

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