Ciro Santilli @cirosantilli 37

Linear map of two variables.

More formally, given 3 vector spaces X, Y, Z over a single field, a bilinear map is a function from:that is linear on the first two arguments from X and Y, i.e.:Note that the definition only makes sense if all three vector spaces are over the same field, because linearity can mix up each of them.

The most important example by far is the dot product from ${\mathbb{R}}^n\times {\mathbb{R}}^n\to \mathbb{R}$, which is more specifically also a symmetric bilinear form.

Implies antisymmetric multilinear map.

For an example with context, have a look at E. Coli K-12 MG1655 and the second protein of the genome, e. Coli K-12 MG1655 gene thrA.

The period does depend on the initial height/angle, except for the very small angle approximation:

In 2019, a paper proved that MTG is Turing complete with a legacy legal deck. Live demo with some hand waving: Video "I Built a COMPUTER in Magic: The Gathering by Because Science (2019)". As Ciro Santilli comments at: github.com/cirosantilli/cirosantilli.github.io/issues/42 this was an interest addition to the previous "indefinite infinite loop" e.g. as found in a Four Horsemen combo deck

On github.com/cirosantilli/china-dictatorship:

Given a linear operator $A$ over a space $S$ that has a inner product defined, we define the adjoint operator $A^{†}$ (the $†$ symbol is called "dagger") as the unique operator that satisfies:

Most commonly refers to: exponential map.