Thank you for making this, finally I get a concrete, visual intuition of what positive definiteness means!
@VisuallyExplained2 жыл бұрын
You are very welcome. Thanks for the nice comment!
@light_rays2 жыл бұрын
The animations are so beautiful! And the geometric intuition was new to me, I like how it also gives a picture for positive linear functionals.
@VisuallyExplained2 жыл бұрын
Thank you so much for the very nice comment, stay tuned for more!
@mspy29892 жыл бұрын
Lol you literally uploaded this video the day before my convex optimization exam. Thanks!
@VisuallyExplained2 жыл бұрын
Awesome!!!! Good luck for your exam!
@piyukr2 жыл бұрын
Finally I got a geometric intuition of what positive definiteness means. Very well explained! Thank you so much.
@MayankGoel4472 жыл бұрын
This is the best video out there to explain Positive Semidefinite Matrices! I finally understood what Positive Definiteness means visually after struggling with the topic for a long time.
@tiga7659 Жыл бұрын
Amazing video! After years of studying at uni I finally understood the real intuition behind Positive definite matrices. Thank you so much! :D
@tsunningwah3471Ай бұрын
😅😮😢🎉
@krishnasinghrajput420611 ай бұрын
How and why is this channel so underrated. The quality of work is one of the finest.
@abdulazizalhaidari76657 ай бұрын
What a great effect your videos have on the course of understanding of many people,
@moopoo1232 жыл бұрын
This is a BEAUTIFUL video. I am floored by your animations and how you communicated the relevance of PSD matrices.
@josecarlosferreira4942 Жыл бұрын
Quadratic functions f(x) = x'Qx, (x is a vector and Q is a matrix), you can consider a symmetric matrix, because: x'Qx is a scalar, so x'Qx = (x'Qx)^T (transpose) x'Qx = x'Qx /2 + (x'Qx)^T / 2 = x'(Q+Q^T)x A=Q+Q^T A is symmetric because A=A^T, so f(x) = x'Ax, where A is symmetric independently of Q
@anjishnu86432 жыл бұрын
Thanks a lot for uploading this. I had been searching for a visual explanation on the topic for a long time. Also, really well explained.
@VisuallyExplained2 жыл бұрын
Thank you very much. :)
@jonasulmen53322 жыл бұрын
huge fan!
@VisuallyExplained2 жыл бұрын
Hooray! :)
@praticandomatematica2462 жыл бұрын
Such a great explanation! I have never read a more clear definition of positive definite matrix.
@pauledam2174 Жыл бұрын
Boom! What a great way to start out -with a single element matrix were the element is a positive number. Fantastic!
@user-ey1dg4xn2u2 жыл бұрын
Please keep making videos. So helpful and intuitive!
@VisuallyExplained2 жыл бұрын
Thank you! Will do!
@ClearMath12 жыл бұрын
My God, you've done an amazing job! I Hope you'll continue to grow, we Need more channels like this to Give credit to this beautiful topics with so smooth animations!
@VisuallyExplained2 жыл бұрын
Thank you so much 😀 I checked your channel and you are doing such fine work yourself!
@arcmchair_roboticist2 жыл бұрын
Wow this is an amazing video and a great channel!
@VisuallyExplained2 жыл бұрын
Thank you so much!!
@accountname10472 жыл бұрын
This is a fantastic video
@VisuallyExplained2 жыл бұрын
This is a fantastic comment!
@tylerperini Жыл бұрын
This is an amazing series, and I look forward to sharing this with my students!
@VisuallyExplained Жыл бұрын
Please do!
@hansenmarc2 жыл бұрын
I ran across positive semidefinite matrices while studying machine learning, but never had a good intuition about them. Thank you for providing some conceptual insight into them.
@potatooflife86032 жыл бұрын
this is amazing. thank you.
@stephaniedsouza30422 жыл бұрын
I am sleepy and tired but this was still an awesome watch
@CHUAN-CHI9 ай бұрын
Absolutely wonderful.
@bitflop2 жыл бұрын
Such beautiful and clear explanations. You are a legend in the making!
@VisuallyExplained2 жыл бұрын
Thank you Ario!!
@MohammadRamadan-o5c2 ай бұрын
Brilliant explanation!
@georgesms Жыл бұрын
WOW! THAT WAS AWESOME!
@danielx19122 жыл бұрын
Amazing amazing videos, cannot say how much I appreciate this!
@VisuallyExplained2 жыл бұрын
Thank you!
@michaelho5138 Жыл бұрын
This is a really great video-love the vibe from the music and timing at the end 😂
@taotaotan56712 жыл бұрын
Awesome. I only encountered this concept from the error message when I am trying to generate some multivariate Gaussian random number with a specified covariance matrix. Nice to see the formal definition!
@user-yk2zu5px3u2 жыл бұрын
thank you so so so much; ive been using the definition of positive definite for so many courses but I never understood why/how it is used i just merely did the calculation it's almost like a eureka for me thank you!!!!
@VisuallyExplained2 жыл бұрын
Great to hear!!
@andres_camarillo3 ай бұрын
Amazing video. Thanks!
@MaiNguyen-yp1sj2 жыл бұрын
wow, best explanation on positive definite that I can find. Thank you so much
@VisuallyExplained2 жыл бұрын
You're very welcome!
@vasanthakumarg453810 ай бұрын
Explanation and animations are really great. keep up the good work.
@amirreza088 ай бұрын
Just WOW! What a great explanation.Thank you!
@giominor882 жыл бұрын
This is amazing. I would love to see some "visual" explanation of SDP relaxations a la Lassere.
@ZhanCaitao2 жыл бұрын
Nice video!
@lithiumdeuteride2 жыл бұрын
Excellent video. Clear, concise, and illuminating.
@VisuallyExplained2 жыл бұрын
Much appreciated!!!
@pp-xc8kb2 жыл бұрын
I cannot say anything more than amazing video! Thank you for your huge contribution!
@VisuallyExplained2 жыл бұрын
Thanks! Glad this was helpful!
@fadi.almasalmah Жыл бұрын
what a wonderful explanation! keep going!
@davidsal83082 жыл бұрын
Awesome video!
@fishinker Жыл бұрын
So good, thank you
@priyankajain16912 жыл бұрын
Nicely explained. Thank you
@jayantnema96102 жыл бұрын
totally love your work dude!
@jkgan49527 ай бұрын
Great Video! Thank you so much :))))))))))))))))))
@sebastianmezaurotadze25812 жыл бұрын
awesome video
@ocamlmail2 жыл бұрын
Tremendously cool explanation, thank you very much!
@VisuallyExplained2 жыл бұрын
You're very welcome!
@igalleikin50402 жыл бұрын
Amazing
@proloycodes2 жыл бұрын
nice animations!
@yahavx Жыл бұрын
What's the visual meaning of x^T*A*x?
@wokeclub1844 Жыл бұрын
Excellent video illustration. But can someone tell me how at 8:23 he gets eigenvalues 1+x and 1-x?? I got them as 1-/+ sqrt(2*x) Pls help!
@VisuallyExplained Жыл бұрын
Thank you! It’s hard to point you in the right direction if you don’t explain how you found these eigenvalues, but Here is a sanity check you can do: the sum of the eigenvalues should be equal to the trace (i.e., the sum of the diagonal elements), and the product of the eigenvalues should be equal to the determinant.
@omridrori32862 жыл бұрын
Can you make also on backprop ? But please do with matricess
@jimlbeaver2 жыл бұрын
Wow, a light bulb for me turned on with this…thanks very much!
@VisuallyExplained2 жыл бұрын
Great to hear!!!
@NoNameAtAll22 жыл бұрын
is there a name for "good solution to NP-hard problem" problems?