Ciro Santilli @cirosantilli 37

The channel is also notable for the fact that the author makes his own music.

Metric space but where the distance between two distinct points can be zero.

Notable example: Minkowski space.

Open source MtG engine implementation written in Java.

Seems to have an option to download art from internet as well.

Ciro Santilli wonders how legal it is. They very explicitly do not mention the words Magic: The Gathering anywhere.

Their UI does a good job at being self explanatory. Space is the shortcut to skip phases.

No online play.

TODO it appears to parse card functionality out of the human readable text! That's genius, as it helps automatically get new cards working, and squirt around legal issues.

A parameter that you choose which determines how the algorithm will perform.

In the case of machine learning in particular, it is not part of the training data set.

Hyperparameters can also be considered in domains outside of machine learning however, e.g. the step size in partial differential equation solver is entirely independent from the problem itself and could be considered a hyperparamter. One difference from machine learning however is that step size hyperparameters in numerical analysis are clearly better if smaller at a higher computational cost. In machine learning however, there is often an optimum somewhere, beyond which overfitting becomes excessive.

For the typical case of a linear form over ${\mathbb{R}}^n$, the form can be seen just as a row vector with n elements, the full form being specified by the value of each of the basis vectors.

Solution $Z$ for given $X$ and $Y$ of:where $e$ is the exponential map.

If we consider just real number, $Z=X+Y$, but when X and Y are non-commutative, things are not so simple.

Furthermore, TODO confirm it is possible that a solution does not exist at all if $X$ and $Y$ aren't sufficiently small.

This formula is likely the basis for the Lie group-Lie algebra correspondence. With it, we express the actual group operation in terms of the Lie algebra operations.

Notably, remember that a algebra over a field is just a vector space with one extra product operation defined.

Vector spaces are simple because all vector spaces of the same dimension on a given field are isomorphic, so besides the dimension, once we define a Lie bracket, we also define the corresponding Lie group.

Since a group is basically defined by what the group operation does to two arbitrary elements, once we have that defined via the Baker-Campbell-Hausdorff formula, we are basically done defining the group in terms of the algebra.

Integrable functions to the power $p$, usually and in this text assumed under the Lebesgue integral because: Lebesgue integral of $L^p$ is complete but Riemann isn't