Ciro Santilli @cirosantilli 37

Intuition, please? Example? mathoverflow.net/questions/278641/intuition-for-symplectic-groups The key motivation seems to be related to Hamiltonian mechanics. The two arguments of the bilinear form correspond to each set of variables in Hamiltonian mechanics: the generalized positions and generalized momentums, which appear in the same number each.

Seems to be set of matrices that preserve a skew-symmetric bilinear form, which is comparable to the orthogonal group, which preserves a symmetric bilinear form. More precisely, the orthogonal group has:and its generalization the indefinite orthogonal group has:where S is symmetric. So for the symplectic group we have matrices Y such as:where A is antisymmetric. This is explained at: www.ucl.ac.uk/~ucahad0/7302_handout_13.pdf They also explain there that unlike as in the analogous orthogonal group, that definition ends up excluding determinant -1 automatically.

Therefore, just like the special orthogonal group, the symplectic group is also a subgroup of the special linear group.

This would be a dream, but it is also impossible: how can you reconcile automated tasks that are simulated quickly like batch crafting 20 muffings in 30 in-game minutes, with someone who is at the same time fighting a hoard of zombies and taking one action every 2 in-game seconds? Alas.

More important than the monk itself in Chinese culture, it is used as a Budhist Amen. TODO find some usage in some Chinese television series.

Bagic jump between orbitals in the Bohr model. Analogous to the later wave function collapse in the Schrödinger equation.

Causality and quantum jumps are incompatible.

As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.

Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix $M$ which encodes the value for each possible pair of basis vectors.

In terms of that matrix, the form $B(x,y)$ is then given by:

It's great right? You can't link to your other answer alone: Stack Overflow link-only answer policy, but you can't copy the other answer either.

And because not all duplicate close votes succeed, see e.g. stackoverflow.com/questions/59649238/how-to-use-the-m5ops-in-gem5-such-m5-exit-and-m5-dump-stats-in-se-mode/63955139#63955139 the result is that someone else will come and answer the same thing in a different wording.

And some answers answer two questions that are not duplicates, e.g. superset/subset questions.

So just do a slight variation wording yourself and get all the reputation.

Related:

A proton or a neutron.