Ciro Santilli @cirosantilli 40

This dude is generally viewed as a God. His incredibly understated demeanor and tone certainly help.

If $C$ is the change of basis matrix, then the matrix representation of a bilinear form $M$ that looked like:then the matrix in the new basis is:Sylvester's law of inertia then tells us that the number of positive, negative and 0 eigenvalues of both of those matrices is the same.

Proof: the value of a given bilinear form cannot change due to a change of basis, since the bilinear form is just a function, and does not depend on the choice of basis. The only thing that change is the matrix representation of the form. Therefore, we must have:and in the new basis:and so since:

Related:

The general result from eigendecomposition of a matrix:becomes:where $O$ is an orthogonal matrix, and therefore has $O^{-1}=O^T$.

See: eigenvalues and eigenvectors.

Electronic Ink such as that found on Amazon Kindle is the greatest invention ever made by man.

Once E Ink reaches reasonable refresh rates to replace liquid crystal displays, the world will finally be saved.

It would allow Ciro Santilli to spend his entire life in front of a screen rather in the real world without getting tired eyes, and even if it is sunny outside.

Ciro stopped reading non-code non-news a while back though, so the current refresh rates are useless, what a shame.

OMG, this is amazing: getfreewrite.com/

Contains the path to the dynamic loader, i.e. /lib64/ld-linux-x86-64.so.2 in Ubuntu 18.10. Explained at: stackoverflow.com/questions/8040631/checking-if-a-binary-compiled-with-static/55664341#55664341

The Wikipedia page of this article is basically a masterclass why Wikipedia is useless for learning technical subjects. They are not even able to teach such a simple subject properly there!

Bibliography:

The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.

In particular, the divergence and the Laplacian can be succinctly expressed in this notation:

In order to express partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variables with indices such as $x_0$, $x_1$, $x_2$, ${\partial }_0$, ${\partial }_1$ and ${\partial }_2$ instead of the usual letters $x$, $y$ and $z$.

Generally, if something is labelled as "e-learning", it's not a good sign, as it implies that it adheres to the "teacher"/"student" separation which Ciro Santilli much despises: E-learning websites must allow students to create learning content.

In the context of Maxwell's equations, it is vector field that is one of the inputs of the equation.

Section "Maxwell's equations with pointlike particles" asks if the theory would work for pointlike particles in order to predict the evolution of this field as part of the equations themselves rather than as an external element.

Measured in amperes in the International System of Units.

As of the 20th century, this can be described well as "the phenomena described by Maxwell's equations".

Back through its history however, that was not at all clear. This highlights how big of an achievement Maxwell's equations are.