Linear Algebra 2j: Elements of ℝⁿ as Vectors - So Boring, yet so Important!

preview_player
Показать описание
Рекомендации по теме
Комментарии
Автор

It's like I am stunned by the things which I have overlooked. The co-relations are so nicely portrayed 

rahulthankachan
Автор

I appreciate how he emphasizes the difference between the 3 types of vector. It's so easy so switch back and forth between #1 and #3, that it's easy to miss the homomorpism.

MathAdam
Автор

First class. Enjoys Mathematics, describes it accurately and coherently, and conveys a sense of awe at the abstraction which Linear Algebra articulates.

etienne-victordepasquale
Автор

Thank you for these videos Pavel! I'm really enjoying this series and learning a lot after having really struggled with linear algebra in the past, in particular the relationship between the three types of vectors. You are an excellent communicator and your explanations are wonderfully clear. I'm looking forward to taking on the tensor calculus playlist after this one!

jal
Автор

this is really useful material, a great lecturer!!!

lauramog
Автор

Pavel, you made me smile - when you say, 'marvel' at triplets. I am a fan of Calculus(and Fourier), do signal processing so applied mathematics is required in my profession. I am going through the videos because I didn't learn math the way American schools teach, and I am prepping myself to help my kids. Your videos go to show that a good teach can make you love Algebra (it's an utterly beautiful topic anyway). I also paint and once wanted to correlate music + painting so your first video just blew my mind. Thank you.

UmaKelkar
Автор

Thank you for sharing these videos. So elegant and insightful.

OtterMorrisDance
Автор

These videos are very useful. I'm preparing to learn tensors and abstract algebra. I'm very interested in their applications for general relativity (especially for black holes and wormholes) as well as quantum mechanics and the hermiticity of operators. I would also like to study algebraic topology in the future.

ibmwatson
Автор

0:58 : The Importance of Rn (3 reasons)
2:08 : Addition
2:45 : multiplication
3:19 : IMPORTANT : the "tivities" are satisfied
3:43 : "being stuck" in a subset
6:55 : the "spirit" of LA : focusing on what all these objects have in common

antonellomascarello
Автор

maybe something out of scope, but I can't understand why orthogonal functions are orthogonal, where is the 90 degree and what is the proof of integration of the products of two orthogonal function is equal zero

ENGAhmedBhje
Автор

Interestingly enough, looking ahead, since the only sub-spaces of R^3 are the origin, a line through the origin, a plane through the origin, and the space R^3 itself, the vectors described by the set V = { (a, b, 3a) : a, b in R } must be either a line or a plane through the origin (clearly V is not the origin and not R^3 itself). It turns out V is a plane through the origin, spanned by the vectors { (1, 0, 3), (0, 1, 0) }, as we can see (a, b, 3a) = a ( 1, 0, 3) + b( 0, 1, 0). But i do see your point, we ought to divorce R^n from geometric considerations (the associated Euclidean space E^n), since strictly speaking R^n are just lists of numbers.

maxpercer
Автор

This is really good but i'm suprised by the order of approaching subjects. It very much flies in the face of convention.

BmCC
Автор

why is seven one of your favorite numbers?

sigmatau
Автор

At 1:23, he says that when we study component spaces, we'll see that all vector spaces are equivalent to Rn. I'm on video 71 right now, but I don't think we've gotten to that yet. Does anyone know what that theorem is or in which video he talks about that? I have a feeling it's like Cayley's theorem in group theory.

grantsmith
Автор

Would you gain more support if I continued commenting on videos or would it be better for me to go on your site?

UnforsakenXII
Автор

I always thought of three dimensions as being intuitive :(

ShwetankT
Автор

this guy is still replying to his previous work

Whatever-jmul
Автор

lol "oh boy" when it came to multiplying 7 and 12 XD

henryalferink
Автор

Thank you for sharing. Stressing on words in sentences over and over makes it sound not pleasant to the ear.

elchinmustafayev