Sometimes it just feels like Ubuntu devs don't actually use Ubuntu as a desktop.

Some extremely annoying problems are introduced and just never get fixed, even though they feel so obvious!

Would never happen on Mac...

This BS started after the move to ZFS. The temporary solution appears to be: askubuntu.com/questions/1293685/out-of-space-on-boot-zpool-and-cant-run-updates-anymore/1374204#1374204

And then this to disable automatic snapshots in the future: askubuntu.com/questions/1233049/disable-automatic-zsys-snapshots-zfs-on-root/1279593#1279593

God, this is so annoying:

math.stackexchange.com/questions/41706/practical-uses-of-matrix-multiplication/4647422#4647422 highlights deep learning applications.

Ciro Santilli found out that he likes computer security researchers and vice versa.

It's a bit the same reason why he likes physicists: you can't bullshit with security.

You can't just talk nice and hope for people to belive you.

You can't not try to break things and just keep everyone happy in their false illusion of safety.

You can't do a half job.

If you do any of that, you will get your ass handed to you in a little gift bag.

All of this is closely linked to Ciro Santilli's self perceived creative personality and being naughty and creative are correlated.

Legal issues stalled them at the turning point of the Internet, and Linux won. Can't change history.

Did Apple just fork it and made Mac OS X without giving anything back?

See: eigenvalues and eigenvectors.

Every invertible matrix $M$ can be written as:where:Note therefore that this decomposition is unique up to swapping the order of eigenvectors. We could fix a canonical form by sorting eigenvectors from smallest to largest in the case of a real number.

Intuitively, Note that this is just the change of basis formula, and so:

The main interest of this theorem is in classifying the indefinite orthogonal groups, which in turn is fundamental because the Lorentz group is an indefinite orthogonal groups, see: all indefinite orthogonal groups of matrices of equal metric signature are isomorphic.

It also tells us that a change of basis does not the alter the metric signature of a bilinear form, see matrix congruence can be seen as the change of basis of a bilinear form.

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 $A$ are $1$ and $4$, and the associated eigenvectors are:symPy code:and from the eigendecomposition of a real symmetric matrix we know that:

Now, instead of $P$, we could use $PE$, where $E$ is an arbitrary diagonal matrix of type:With this, would reach a new matrix $B$:Therefore, with this congruence, we are able to multiply the eigenvalues of $A$ by any positive number $e_1^2$ and $e_2^2$. 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 $D$ does not have to contain eigenvalues, unlike the eigendecomposition of a matrix. This is because here $S$ is not fixed to having eigenvectors in its columns.

But because the matrix is symmetric however, we could always choose $S$ to actually diagonalize as mentioned at eigendecomposition of a real symmetric matrix. Therefore, the metric signature can be seen directly from eigenvalues.

Also, because $D$ 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.

Related:

For this sub-case, we can define the Lie algebra of a Lie group $G$ as the set of all matrices $M\in G$ such that for all $t\in \mathbb{R}$:If we fix a given $M$ and vary $t$, we obtain a subgroup of $G$. This type of subgroup is known as a one parameter subgroup.

The immediate question is then if every element of $G$ can be reached in a unique way (i.e. is the exponential map a bijection). By looking at the matrix logarithm however we conclude that this is not the case for real matrices, but it is for complex matrices.

Examples:

TODO example it can be seen that the Lie algebra is not closed matrix multiplication, even though the corresponding group is by definition. But it is closed under the Lie bracket operation.

The OS that the Gods ordered be made.

One is reminded of Ulillillia, see also: www.youtube.com/watch?v=9-79yOZ13qg The Story of Ulillillia by Atrocity Guide (2019)

We are all somewhere in the spectrum.

www.velp.com/en/products/lines/3/family/44/vortex_mixers/65/wizard_ir_infrared_vortex_mixer (archive).

The cause of variable number tandem repeat.

The real explanation: stackoverflow.com/questions/1780599/what-is-the-meaning-of-posix/31865755#31865755

Overview by Ciro Santilli at: superuser.com/questions/284342/what-are-path-and-other-environment-variables-and-how-can-i-set-or-use-them/1864687#1864687