Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.

This video really helped tie these concepts together for me. I really appreciate your posting it.

this is so cool. Love this channel. I'm learning so much I should have learned years ago.

I have to say that I love your voice, and the passion you have for the subject.

@joshuaronisjr

5 жыл бұрын

He talks a little like Feynman

To understand the least square derivation, I check this. Super helpful !!!

Why does he talk like hes trying to get me to recapture the means of production from the bourgeoisie?

@MathTheBeautiful

4 жыл бұрын

Because he is lenin in that direction

Great lecture he explains so well.

Made this concept easy to understand, thank you!

For your gradient descent, do you need the -b in there, eg x -> x - a(Ax-b) ? It seemed without that -b and a positive definite matrix A, zero is the only solution. But with -b then -1,-2,4 is the solution.

@MathTheBeautiful

7 жыл бұрын

Yes, you are correct!

Great video. This was explained very intuitive.

1:18 Just as an observation, while it is usual to see the quadratic form as presented here, I find the following a little bit more ... elegant: 0.5 * [W] {x y z 1} With a line vector, { } a column vector and [ ] a matrix. Here W = 4 1 2 -2 1 8 5 -3 2 5 4 -4 -2 -3 -4 0 symmetric if A is symmetric. Note that the minus sign for the last column and the last line is due to the original subtraction. The 0 stands when the constant term is ... zero.

great way of explaining quadratic optimization

Excellent teacher! and Life saver

Gradient descent is a technique used in machine learning nowadays to optimize a loss function . This video is great

Thanks for this awesome video

Thank you, so clear!

Monster of Math.

where i can found the statement ? i did an unsuccessful search

This really helps a lot in understanding matrix derivative, and it's so clear. Thanks!!!

Great explanation!! Thank You

@MathTheBeautiful

3 жыл бұрын

Glad it was helpful!

thank you!

I love this guy

Awsome. Thank you.

@MathTheBeautiful

Жыл бұрын

Thank you!

7:15 what if your matrix is positive semi-definite? Wouldn't there be a minimum?

I always knew that something was off with this derivation. I am relieved that this wasn't because of my lack of talent in math.

@MathTheBeautiful

4 жыл бұрын

It's **never** you. It's always the textbook.

thank you, it was a beautiful course

@MathTheBeautiful

7 жыл бұрын

Thank you, Ali, I'm glad you're enjoying our videos. But why "was"?

@AliVeli-gr4fb

7 жыл бұрын

MathTheBeautiful it is normal to say it in past tense in my language, so I thought in it, but wrote in English. so no real reason

@MathTheBeautiful

7 жыл бұрын

:) I just wanted to convey that the course is ongoing!

@TheTacticalDood

5 жыл бұрын

@@MathTheBeautiful Is it still ongoing? This channel is amazing, it would be sad to see it stop!

Nice explanation sir You look like Jason Statham ❤️❤️❤️ I felt like action star is giving lecture on matrix❤️❤️🙏

@MathTheBeautiful

3 жыл бұрын

I get that a lot when I wear a tight t-shirt.

SIR - U R VERY CLEAR =PLEASE GIVE SHORT LECTUR

Is there a relation between positive definite matrix and convex set

@MathTheBeautiful

3 жыл бұрын

Yes, excellent intuition. The level set for a positive-definite quadratic form is a convex shape.

I wont examples or meteial to illusstrate the idea of method of maximization and minimaization of function with constraint(lagrage multiplier ) and with no constraint(by quadratic form and hessian matrex) 😭

This is just a comment for me to look at in the future, but at some point, he says that A will mostly be filled with zeroes before we start Gaussian elimination. A will be the covariance matrix, (X^T X) (look at the next video, the least squares solution video). That it's mostly filled with zeroes indicates that most of the random variables (each column of X is a different random variable of the dataset) are independent of one another (or at least, if they ARE independent then their covariance will be 0). However, Gaussian elimination involves linearly combining rows. The matrices in between may NOT be sparse! As for computer storage...I don't know much about it, but maybe computers store zeroes in a different way, so that sparse matrices are easier to store? Actually, I guess this comment is more than for just me...why can computers store sparse matrices well?

Absolute value has a minimum.

At 13:15 my chin literally felt

@ElizaberthUndEugen

4 жыл бұрын

*dropped

Why skip the matrix calculus? It's not rocket science