Lecture 3: Multilinear Algebra (International Winter School on Gravity and Light 2015)

As part of the world-wide celebrations of the 100th anniversary of Einstein's theory of general relativity and the International Year of Light 2015, the Scientific Organizing Committee makes available the central 24 lectures by Frederic P Schuller.
Titled "A thorough introduction to the theory of general relativity", the lectures introduce the mathematical and physical foundations of the theory in 24 self-contained lectures. The material is developed step by step from first principles and aims at an audience ranging from ambitious undergraduate students to beginning PhD students in mathematics and physics.
Satellite Lectures (see other videos on this channel) by Bernard F Schutz (Gravitational Waves), Domenico Giulini (Canonical Formulation of Gravity), Marcus C Werner (Gravitational Lensing) and Valeria Pettorino (Cosmic Microwave Background) expand on the topics of this central lecture course and take students to the research frontier.
Access to further material on www.gravity-and-light.org/lectures and www.gravity-and-light.org/tutorials

[@EarlWallaceNYC]

I'm loving these lectures.
They are rigorous, well organized and entertainingly presented.
Where else can I find a reverence to Machiavelli in advanced mathematics.

[@eenblanke]

Fantastic lectures! This is the way it should be done . So clear, concise and even entertaining at time. German efficiency and thoroughness shows through. Thanks so much to the folks that posted it

[@junhyukkang9100]

This is the most thorough explanation of the vector space I have ever heard (13:43). Thank you for the nice lecture.

[@travellcriner6849]

I have been watching the videos up to this point. These videos are amazing and the material is extraordinarily well-explained. That is not to be taken lightly as I am young math major who has currently taken no physics courses and math courses only up to Calculus 1. (I admit, though, I have watched and read an abundance of math and physics in my free time). My point is, if I understand this stuff sufficiently [though I admit I had to rewatch the explanation as to why a (1,1)-Tensor is equivalent to a Vector-Valued function of a Vector Variable SEVERAL times] with my lack of formal education, it's superbly explained.
I look forward to the rest of the series!

[@rajanalexander4949]

Such a clear, engaging and well-paced exposition. Who thought a lecture on tensors could be so entertaining?
Thank you!

[@jwp4016]

What a monstrously brilliant explanation...!! It's a shame that I've never seen a single math professor comparable to him, even on materials quite elementary like this. Does anyone know his name?

[@jwp4016]

Frederic p. schuller

[@mapleandsteel]

You are just awesome, Professor !

[@MaxwellsWitch]

I love it when you give the axioms first before you start calculating shit, that removes ambiguity and confusion. thx m8.

[@time_traveller24]

Thank you sir...your lectures were extraordinary

[@LibertyAzad]

Where is Paris + Vienna? Hmm, never thought of that one.

[@zawette]

are there anymore videos about bilinear algebra ? i couldn't find anything on TH-cam

[@deleogun1717]

thank you

[@jaksaf1234]

Anyone know where I can find the problem sets that accompany these lectures?

[@ErnestYAlumni]

+Jak Safin github.com/ernestyalumni/Gravite/blob/master/LaTeXetpdfs/WEHeraeus/tensors_neu.pdf for this lecture; I'll put up what I was able to download when I can on my github

[@pianoman1857]

For the first example how can he define the set P as linear combinaison of whatever element whithout define an add and mult law on x^n ?

[@rubenlimasca4488]

Muy fácil.