Orthogonal sets

This is the first video of a linear algebra-series on orthogonality. In this video, I define the notion of orthogonal sets, then show that an orthogonal set without the 0 vector is linearly independent, and finally I show that it's easy to calculate the coordinates of a vector in terms of an orthogonal basis. Enjoy!

[joaovictormacedosales]

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

[MrCigarro]

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

[proalexv]

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!

[kamoroso]

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.

[AlexiLaiho]

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.

[norman.]

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

[TheMauror]

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!

[franciscojavierorozcobeiza]

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

[LeilaS]

I like your enthusiasm. You creat hope🌷

[Myuri]

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

[renzalightning]

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

[weinihao]

so cool, orthogonality is also one of my favorites!

[tonyantonio]

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

[cubicardi]

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

[JPK]

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 :)

[sansamman]

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

[michaelempeigne]

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.

[vanessakitty]

Chalk and talk is an old favorite method of mine.

[jeromesnail]

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!

[omrimg]

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