Ciro Santilli @cirosantilli 37

Analogous to a linear form, a bilinear form is a Bilinear map where the image is the underlying field of the vector space, e.g. ${\mathbb{R}}^n\times {\mathbb{R}}^m\to \mathbb{R}$.

Some definitions require both of the input spaces to be the same, e.g. ${\mathbb{R}}^n\times {\mathbb{R}}^n\to \mathbb{R}$, but it doesn't make much different in general.

The most important example of a bilinear form is the dot product. It is only defined if both the input spaces are the same.

Since DNA is the centerpiece of life, Ciro Santilli is extremely excited about DNA-related technologies, see also: molecular biology technologies.

TODO examples:

youtu.be/Ca7c5B7Js18?t=803 compares Lagrangian mechanics equation vs the direct x/y coordinate equation.

Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.

Paraprasing a friend of Ciro Santilli:

Luckily, early teens Ciro Santilli was partly protected from this by Ciro Santilli's cheapness.

But Ciro distinctly remembers one day in his early teens that he couldn't sleep very well, and he got up, and the was decided that he would become the greatest Magic: The Gathering player who ever lived. Can you imagine the incredible loss that this would have been to humankind? And talk about the incredible lack of development opportunity present in poor countries, related:

The key is to define only the minimum number of measures: if you define more definitions become over constrained and could be inconsistent.

Learning the modern SI is also a great way to learn some interesting Physics.

The author seems to have uploaded the entire book by chapters at: www.physics.drexel.edu/~bob/LieGroups.html

And the author is the cutest: www.physics.drexel.edu/~bob/Personal.html.

Overview: