Linear Algebra: Norm

In this video, we discuss the idea of Norm and how it relates to vectors.
00:00 - Introduction
00:12 - Definition of Norm
02:11 - Properties of Norm
05:45 - Unit vectors
07:00 - Example 1
08:14 - Example 2
09:12 - Example 3
10:00 - Normalization
12:51 - Example 4
16:18 - Unit vector and direction
17:59 - Example 5
22:34 - Example 6
28:36 - Norm interpreted geometrically

[@rudolfmosoma9364]

Short and simple.. You such a great teacher, wonder if you will be assisting with Stats and Discrete Mathematics 😭😭

[@pinkkitty6553]

fancy way of saying magnitude of vector, thanks that cleared a lot of doubts.

[@sinajalali8974]

Well explained. I understand it now. Thank you

[@rishiraj6602]

Very clearly explained, thank you :)

[@mixerbd791]

Nice explanation and presentation.
Thanks Sir.
Love feom Bangladesh.

[@Mohammad_alhayajneh]

Thanks alot bro ,you are explain it very smooth and easy ,i appreciate your effort ❤

[@MathforThought]

Thanks!

[@enass.muhammed7469]

Thank You so much, you have a unique and organized way in explaining the subject!!!

[@MathforThought]

Thank you!!

[@vincentmudimeli4430]

man your lesson make maths especially complex concept like matrx look easy thanks keep the good wwork going

[@MathforThought]

Thank you so much!

[@memit0]

Thank you broski you are amazing!!

[@hayyan_azzam]

i pay so much for uni just to find better explaination on yt for free, thank you

[@MathforThought]

Thank you!

[@garnikmikayelian4271]

Thank you so much, everything was very clear. You really helped me ✍️✍️

[@bilecode8114]

Great guy!. you must be appreciated buddy.....

[@EngrSajeed]

God bless you you deserve likes

[@yufeiliu1596]

thanks a lot

[@Mar1lyn02]

Sucks that, this video is watched too few. Thanks for the good effort mister!

[@MathforThought]

Thanks!

[@MathwithWaqasShah]

nice lecture sir .

[@MathforThought]

Thanks!

[@manav11142]

How to imagine an n dimensional triangle? To apply the pythagorus thm

[@MathforThought]

You just take the square root of the difference of each component square.

[@ghassanebrabish8255]

Hey man so for Ex 6 why point M would not just be equal 2/5*(PQ)?

[@MathforThought]

M is a point. Not a vector. It doesn't really make sense to say a point 2/5th of the way. You could say a direction vector is 2/5th of the way though. M as a point has to be in reference to something in order to make sense of which way it's going.

[@-mwolf]

So I saw the norm definition of ||x|| subscript p = sum of all x^p and then taking the pth root of that. Could you explain what the p stands for? Is it the norm in higher dimensions?

[@MathforThought]

Sorry could you point out where I did that? I can't find the timestamp.

[@-mwolf]

@@MathforThought No, you only did it in this video with ||x||2 = ((x1)²+...+(xn)²)^½ . I was just wondering what it means to have e.g: ||x||3 = ((x1)³ +...+(xn)³))^⅓ But I guess it's just the norm of a vector in a higher dimension? Would have been cool if you mentioned that.

[@MathforThought]

@@-mwolf Ahh I see what you are saying. I didn't use p anywhere in the video but some people do use p as a way to refer to the dimension of the norm yes.

[@-mwolf]

@@MathforThought Thanks!

[@pipertripp]

the Euclidean norm is the "2 norm" and is part of a more general class of norms call "P norms" where:
||v|| = (sum i=1 to n: abs(v_i)^p)^(1/p)
sorry if that's hard to read. The "dot product" that everyone learns in first year physics is the Euclidean norm. The "1 norm" is just the following, based on that formula I wrote above:
||v||_1 = abs(v_1) + abs(v_2) + ... + abs(v_n)
the underscores are subscripts and the carets are super scripts. I hope that that was useful.

[@derjemand1021]

thanks

[@user-bq8ng1fi5b]

perfect

[@Goat_Dips]

A piece of advice: if you're going to do word problems as in 19:25, have them written down beforehand. That would slightly save students' time. Thanks!

[@MathforThought]

Thanks! I didn't do it initially since I didn't know how much space I needed ahead of time.

[@-mwolf]

Just fast forward 5 seconds for as long as he's writing

[@Tareq--ri6qe]

❣️

[@YohanesZakariasRadjaHedo-mr9rj]

Sudah....

[@iqramushtaq2461]

What is the norm of X=[1+1+1+1,,,,,,,1]

[@MathforThought]

You just square root each component squared.