Orthogonal sets 

Better than Netflix series!

I'm taking a linear algebra class right now! We just talked about what it means for a set of vectors to form a basis of ℝ³ today. We've been talking about linear independence, spanning sets, and row reduction in augmented matrices lately. But we haven't talked about orthogonal sets yet. At the end where you showed a=(x•u)/(u•u), etc., it reminds me of the scalar you obtain when projecting one vector onto another, proj_u(v)=((u•v)/(u•u))u. I find the class really interesting, so I'm really excited to follow along with your video series as well! I feel like this kind of math is really powerful.

You're the best, Peyam! Please, even after this series, bring us some more cool topics in linear algebra, like linear operators!

this was a really good one, loved it, thank you! it's good to see some real-life applicable mathematics on here. i want to go to dinner with you or something, you're so likeable.

Excelent video. I found orthogonality very interesting when I took LA a year ago. What blew my mind the most is the Gram-Schmidt method to find an orthogonal set that has also only unit vectors (in Spanish is called 'conjunto ortonormal'). I think its awesome!

I love that saying about the essence of linear algebra. Linear algebra serves as an "Algebraic way of defining a geometric concept" I was just wondering while taking your course what's the big idea or take away, and the same day as I'm thinking about it I hear you say it. Great explanation by the way!

Reciba un saludo y agradecimientos desde Puebla, México. Gracias por esta serie de videos, para nosotros, Estadísticos, esta serie es fundamental.

White shirt so you can't see all the chalk on it?😀

You're really good thanks for UP load videos!!!

Oh man! U hugs itself! I don't know which is more fun now, learning the math or enjoying it !!! super cool Peyam jan! :-)))

Chalk and talk is an old favorite method of mine.

I like your enthusiasm. You creat hope🌷

I remember doing the Gram Schmidt process! It was beautiful!! Can't wait for that one to remind me :D Gonna like this series!!

I actually had my LA final today, part of it was orthogonality! Went nice.

so cool, orthogonality is also one of my favorites!

Haha I love the analogy you gave at 22:17 I will remember this for my Linear Algebra Final this Wednesday :D

I love how you say "Fourier" with the French accent :) I'd love to see a video about difference equations, and why the method to solve them works!

nice idea for a series one little thing: at 13:00 you dont need to do it for v and w after you done u, the relation between the 3 is symmetric also the proof that the span of the set B is Rn iff B contains exactly n L.I. vectors is one of my all times favorite still sick so i couldnt catch up with the videos i missed... BTW... still waiting

first to comment on the first video of a topic on series that is the first to this channel OMG!

Thanks for the great video! For anyone having trouble understanding what linear independence means spatially, look at 3Blue1Brown's Essense of Linear Algebra series. Also, Dr. Peyam, the lighting in this video gets a little weird, especially at 14:30 and 19:30. I don't know if you can fix this by adjusting sensitivity to light, but if you could, that would be awesome for the future :)

Yayyyy fourier series!!(:

I have not seen a proof of orthogonal projections before but I have known about that for a long time. I bought myself a book about this topic and diagonalization of matrices as well. I would like to see a proof and / or definition about Hermitian operators.

I love orthogonality, it makes bases a lot easier to work with

THANK GOD! SUPER HELPFUL

Instead of doing all those dot products to rebase the vector, you could have placed u,v,w into a matrix A = [u,v,w] and multiplied A^-1 * x, which gives the x* that you were looking for. That's treating it like a linear transformation. Calculating A^-1 by hand isn't necessarily all that quick, but on a calculator, this is the way to go.

Yay new video!

Great video, thanks!

Dear Dr. Peyam, can you solve 3^x=3x+1 without brute force?

I once lost a mark on my assignment for writing perpendicular when I meant orthogonal. :(

11:43 if i believe my textbook on dot product properties i have to question the claim: (u dot u) = ||u||^2 = not 0. My textbook says: ||u||^2 >= 0. Zero length can be valid result,it is the origin O(0.0). Also , if (u dot u) = 0 => u = 0.