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Visual Kernel
เข้าร่วมเมื่อ 10 มี.ค. 2022
SVD Visualized, Singular Value Decomposition explained | SEE Matrix , Chapter 3 #SoME2
A video explains Singular Value Decomposition, and visualize the linear transformation in action.
Chapters:
0:00 SVD Intro
1:17 Visualize a Rectangular Matrix ?
5:16 Creating Symmetric Matrix
7:17 Singular Vectors and Singular Values
8:55 SVD Formula Dissection
10:05 The Visualization
12:54 Is this SVD ?
15:16 The Next Journey
Video Sins:
1. Regarding the eigenvectors of symmetric, it is correct to say the eigen vectors are orthogonal if the matrix is full rank. However, the formal definition is there always exist a orthornormal basis which contains the eigen vectors of the symmetric matrix, for details refer to th-cam.com/video/UCc9q_cAhho/w-d-xo.html, where professor Strang explains the case with eigen vectors with eigen value of 0.
2. When S_L or S_R right has eigen values of multiplicity more than 1, there is an entire subspace of them, therefore, we need to put an orthonormal basis of the subspace to sure all the eigen vectors are perpendicular. Of course, this is already getting more involved with the details with the derivation of the SVD formula in the first place, I think I will leave this to the expert: th-cam.com/video/rYz83XPxiZo/w-d-xo.html
This video wouldn’t be possible without the inspiration of the legendary 3b1b :
th-cam.com/users/3blue1brown
and the animation software - Manim, which he wrote:
th-cam.com/users/3blue1brown
and the Manim Community:
docs.manim.community/en/stabl...
Music Credit:
1. Lord of the ring lofi by Sam Cisco: th-cam.com/video/AfIvjUYbie4/w-d-xo.html
2. "First Layer" ost from an anime called Made In Abyss
3. "My War" lofi from AOT, music made by Kijugo th-cam.com/video/oCXIEfHR1Qk/w-d-xo.html
Chapters:
0:00 SVD Intro
1:17 Visualize a Rectangular Matrix ?
5:16 Creating Symmetric Matrix
7:17 Singular Vectors and Singular Values
8:55 SVD Formula Dissection
10:05 The Visualization
12:54 Is this SVD ?
15:16 The Next Journey
Video Sins:
1. Regarding the eigenvectors of symmetric, it is correct to say the eigen vectors are orthogonal if the matrix is full rank. However, the formal definition is there always exist a orthornormal basis which contains the eigen vectors of the symmetric matrix, for details refer to th-cam.com/video/UCc9q_cAhho/w-d-xo.html, where professor Strang explains the case with eigen vectors with eigen value of 0.
2. When S_L or S_R right has eigen values of multiplicity more than 1, there is an entire subspace of them, therefore, we need to put an orthonormal basis of the subspace to sure all the eigen vectors are perpendicular. Of course, this is already getting more involved with the details with the derivation of the SVD formula in the first place, I think I will leave this to the expert: th-cam.com/video/rYz83XPxiZo/w-d-xo.html
This video wouldn’t be possible without the inspiration of the legendary 3b1b :
th-cam.com/users/3blue1brown
and the animation software - Manim, which he wrote:
th-cam.com/users/3blue1brown
and the Manim Community:
docs.manim.community/en/stabl...
Music Credit:
1. Lord of the ring lofi by Sam Cisco: th-cam.com/video/AfIvjUYbie4/w-d-xo.html
2. "First Layer" ost from an anime called Made In Abyss
3. "My War" lofi from AOT, music made by Kijugo th-cam.com/video/oCXIEfHR1Qk/w-d-xo.html
มุมมอง: 214 167
วีดีโอ
Visualize Spectral Decomposition | SEE Matrix, Chapter 2
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A video illustrating the underlying elegant visual interpretation of Spectral Decomposition. Chapters: 0:00 Chapter 1 Summary 1:23 Symmetric Matrix ? 1:44 Property of Transpose 3:27 Matrix Decomposition 4:58 Eigen Vectors and Eigen Values 8:07 Strong Property of Symmetric Matrix 9:36 Spectral Decomposition 12:03 Visualization 14:13 appreciation Video Sins: 1. regarding the eigenvectors of symme...
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Visualizing, identity matrix, scalar matrix, reflection matrix, diagonal matrix, zero matrix, shear matrix, orthogonal matrix, projection matrix, inverse of a matrix. Chapters: 0:00 Visualize Matrix, but how ? 3:07 Identity Matrix 4:02 Scalar Matrix 6:23 Matrix in 3D 7:01 off-one Matrix 8:45 Reflection Matrix 10:54 Diagonal Matrix 14:00 Zero Matrix Hopefully providing more intuition about matri...
Visualize Different Matrices part2 | SEE Matrix, Chapter 1
มุมมอง 41K2 ปีที่แล้ว
Visualizing, identity matrix, scalar matrix, reflection matrix, diagonal matrix, zero matrix, shear matrix, orthogonal matrix, projection matrix, inverse of a matrix. Chapters: 0:00 Shear Matrix 1:57 Orthogonal Matrix 5:20 Projection Matrix 7:30 Inverse 9:35 What exactly is a Matrix ? Hopefully providing more intuition about matrix transformation on vectors and making the very abstract object o...
10:36 - From this on matrix is wrong. You seem to place numbers into the matrix quite randomly.
I have only one complaint. You should have shown how multiplication _Ax_ is actually just a linear combination of column vectors of A, in the proportions given by vector x. Componentwise multiplication process is utterly nonintuitive.
Dude forgot he have yt channel
Saturday morning. Watching this series as a Netflix documentary.
wow simply wow, I have not seen such a beautiful visualization.
excellent, why is this channel not producing more videos like these.
imagine being so good that u can explain matrix composition using a chord in music 3:58. This explanation is itself multidimensional my brain is exploding
Its been 2 years. Where are you bro :’)
great video but here is one error/correction: at 3:16 it is stated that orthogonal matrices produce pure rotations with "no reflection" - this is in fact false - orthogonal matrices can indeed produce reflections. The defining property of an orthogonal matrix is U^T U = UU^T = I; check this property for any reflection matrix and you will find that it is satisfied. Orthogonal matrices can produce both rotations and reflections. Note that in 2D, a product of two reflection matrices is also a rotation matrix.
in case anyone is wondering, the subset of orthogonal matrices that produce pure rotations (not reflections) are those that have determinant(U) = +1 (and with -1 a reflection is additionally involved in general). for orthogonal matrices the determinant is always +/- 1 so this covers all cases.
omg! the made in abyss music in the background made me soooo happy! that's my favorite anime ever! thank you so much for everything, you're helping me pass my 18.06 exam tomorrow! you're the goat!
This is gold
pls come back bro I need a video on PCA asap
How is this free??
Really hope you can make more videos ! The way you explain a concept is so elegant and makes it such a breeze to comprehend.
I LOVE THIS VIDEO
Thanks ! I enjoyed a lot <3
9:00 You have no idea how long I’ve been looking for a clear explanation of orthogonality and it’s practical application. I’ve now read 2 textbooks on la and am reading aa right now, and you are the only person to actaully answer WHY we want orthogonality besides linear independence. You just earned a sub
Useful video - Cheers
Thank you so much for the video. It is really helpful to explain someone with this who do not have their background in linear algebra. Thanks again for all the effort. Its worth it.
Bro you are single handedly save my master degree. thanks
I just fuc**** love this channel, this video, and its creator...❤️🔥, thank you so much for the svd intuion Anna(in my language brother❤️). I just love all the maths community ❤️🔥.
Thank you 🙂🙂
Great work!
Soooo better visual math videos than anyone.... Just subbed bro.
Thank you for making such a fun and informative video!
Crazy!! Thank You !
This was insane. Thank You so much!
Awesome explanation - thank you! Still waiting for the PCA video :)
wow, it was fantastic explanation. could you please do a video on PCA? Thank You
Wait a second? Is the background music the opening song from AOT, My War? 10:14
The music is unexpectedly cool for a Math video
thanks for making me fall in love with math all over again <3
GREAT VIDEO!!! I'm studying this right now and we saw this as some way of change of basis in a way that the transformation be nicer, and also to do these things with approximation of images and to get the most important features of some data. It's great to have that way of geometric visualization too, and makes perfect sense with I have studied.
just loved it !
attack on titan theme in the background goes hard
Sir you are to be congratulated. I am always searching for an understanding of difficult mathematical concepts to be explained simply. You have done that in spades for this difficult concept of linear algebra. Your series of videos that lead up to your SVD explanation are pedagogical genius. Professor Gilbert Strang would be proud.
Such a great video. I am using it in all my Linear Algebra classes next week. Thank you!
goat
goat
hell yeah chapter 6 Attack on Titan lofi. This is my last warrr!
牛
你是中國人？
Amazing. Wow. Fabulous
3:13
Marvin Squares
i wish there is a discord server
I watched your 4 videos in a row. What a breathtaking journey! Are you still working on the video of principal component analysis? Highly looking forward to watching your another masterpiece!
WOW!!!!! It is really amazing!!!!!!! A classmate in my master's degree shared your video and I really liked it!!!! WAW! WAW! I loved the way how you gave example of mario using matrices. JUST WAW!
Murphy Mount
Amazing!