Metric space vs normed vector space vs inner product space by 
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01TODO examples:
- metric space that is not a normed vector space
- norm vs metric: a norm gives size of one element. A metric is the distance between two elements. Given a norm in a space with subtraction, we can obtain a distance function: the metric induced by a norm.
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:
Magic: The Gathering is like cocaine in card form.
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:
Supervised and unsupervised learning by Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01 Feud between Sabine Hossenfelder and Luboš Motl by Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01The 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.
Lie Groups, Physics, and Geometry by Robert Gilmore (2008) by Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01The 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:
- Chapter 3: gives a bunch of examples of important matrix Lie groups. These are done by imposing certain types of constraints on the general linear group, to obtain subgroups of the general linear group. Feels like the start of a classification
- Chapter 4: defines Lie algebra. Does some basic examples with them, but not much of deep interest, that is mostl left for Chapter 7
- Chapter 5: calculates the Lie algebra for all examples from chapter 3
- Chapter 6: don't know
- Chapter 7: describes how the exponential map links Lie algebras to Lie groups
Lagrangian mechanics lectures by Michel van Biezen (2017) by Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01Original playlist name: "PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS"
Author: Michel van Biezen.
High school classical mechanics material, no mention of the key continuous symmetry part.
But does have a few classic pendulum/pulley/spring worked out examples that would be really wise to get under your belt first.
Equivalent to Lagrangian mechanics but formulated in a different way.
Motivation: Lagrangian vs Hamiltonian.
TODO understand original historical motivation, www.youtube.com/watch?v=SZXHoWwBcDc says it is from optics.
Intuitively, the Hamiltonian is the total energy of the system in terms of arbitrary parameters, a bit like Lagrangian mechanics.
Bibliography:
Like Jimmy Wales, he used to work in finance and then quit. What is it with those successful e-learning people??
There are unlisted articles, also show them or only show them.