You've saved my life, Ive been looking for a way to show that a matrix is PSD for days!!

Very simple and efficient, thank you !

Hvala, doktorice!

Very great lecture, thanks.

super explanation.liked it

Thank you very much this helps a lot.

this was really helpful thanks

Thank you teacher!

Thank you teacher

This is great !

most thanks

Thanks

Muito bom!!! obrigado

Thanks a lot! As always straightforward and great!

this is great.

Thank u for your commitment! Great.

what if the determinants of the matrix in the upper-left corners are all zero? still positive semidefinite?

nice video

Good to know how to determine whether a matrix is positiv definite. But what does it mean when a matrix is positiv definite? Why would I want to know this?

@nozirshokirov6974

9 жыл бұрын

In Linear and Nonlinear Programming bunch of theorems are built upon the assumption that a matrix is psd. And you gonna need it a lot if you will have to deal with them.

@trivenitharu4082

9 жыл бұрын

Y

@robertwilsoniii2048

6 жыл бұрын

It’s important for optimizing equations. It turns out that when you have a differential equation, such as setting a derivative equal to zero, your solution set can be made into a quadratic polynomial by subtracting your solution plus h by your solution. It turns out that every quadratic polynomial determines a symmetric matrix. Then, if all the eigenvalues of that matrix are positive, your critical point of your differential equation is a local minimum, if all the eigenvalues of the hessian are negative, your critical point of the differential equation is a local maximum. If you have both positive and negative eigenvalues your critical point of the differential equation is a saddle point. If your critical value of your differential equation is 0, the value is degenerate - indeterminate. You need another way of deciding what that solution means qualitatively. This is *very useful* in engineering of all kinds. I guarantee every company in the tech industry, especially those in the Silicon Valley, heavily use this mathematics on a daily basis in nearly every product or service.

The first test for positive semidefiniteness is wrong but in this case I think her solution is still correct. It isn’t sufficient to check in the 3x3 case just these 3 determinants, you have to check all principal minors not only the leading ones. Take for example the diagonal matrix with the entries 0 and -1 on the diagonals. The determinants/leading principal minors would be 0 and 0(-1)=0 and therefore the matrix should be positive semidefinite, but obviously isn’t.

thank youuu

I know this is old, but just so I can confirm that I understood. The matrix B is only positive semidefinite ONLY when c = 0, and not when c > 0, because then B would be positive definite. Am I correct?

@EdouardCarvalho82

3 жыл бұрын

Not when c=0, but exactly when c>=0. Semi-definiteness allow the =0 case to sneak in the pos. def. like she says.

THANK YOU. My textbook is so bad explaining this bullshit

I REALLY HAVE NO IDEA ABT THIS BUT I NEED TO STUDY THIS

Can somebody explain what happened at 8:35?

@MuddasirJahangir22

6 жыл бұрын

Ok I figured it out. She used the values of Echelon form of B to complete the squares.

I never skip the class if she is my teacher :D lol . thank you

@insightmanners6876

4 жыл бұрын

dasar imam supriadi

MIT makes great videos and course notes. My professor went to MIT and her notes are not very good so I just use MIT's notes for their state space control systems course. I don't know what they hell it is but they do shit right over there.

I need personal tutoring

watch it in big screen for better understanding

falling in love

she has a cute way to say "minus" :DD

@hfgjjhkjjbvkkb3442

7 жыл бұрын

I guess you´re in love.

Why the first det. is 2?

@tayyabrafique21

8 жыл бұрын

+Sami Samim the upper left corner matrix (within the 3x3 matrix) has only one element with nothing in rows or columns so that's why it is det of its own.

are u a bond villain?

for example this one 0 0 -1 0 0 0 -1 0 2 can still use the determinant test? i know that by computing its eigenvalues it's not pos, semi. def. therefore it's not pos. def. either. i just want to confirm determinant test is still applicable for this situation. thanks!

@97Alfinsyah

6 жыл бұрын

maybe you can try sarrus method bro

i will intentionally failed this subject to repeat her classes

Kernel = nullspace

Make tests on me im ready

no offense but he's rite

Who's watchingg video for the teacher, not for learning? :-D

@nagaapi

5 жыл бұрын

me

very great lecturer, but why she hates me lol

She is Russian , and most of the modern mathematics roots back to Russia.

@ParidTvShow1

6 жыл бұрын

the fuck did i just read....

You guys would not get into mit if distracted by a girl lol

Her voice is kinda scary. If I happened to be one of her students, I might get intimidated by her voice.