@the.synthetic.mind: In this video, we track a single two-by-two matrix from start to finish to develop the geometric intuition behind the singular value decomposition. We show why ordinary eigenvalues fail to capture a matrix's maximum stretching factor or its best low-rank approximation, and we derive the full A = U Σ V^T recipe step by step. Finally, we examine how this framework guarantees optimal approximations in image compression, recommendation systems, and principal component analysis. #SingularValueDecomposition #LinearAlgebra #AppliedMathematics #MachineLearning

The Synthetic Mind
The Synthetic Mind
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Monday 19 October 2026 16:22:10 GMT
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lulkas9
Lukas :
everything leads to linear algebra
2026-10-20 05:43:35
163
usersxnnvrjv27
usersxnnvrjv27 :
I've never seen a movie recommendation algorithm that would recommend me a movie accurately
2026-10-20 00:50:44
122
koen50007
User5000 :
just let AI do it in a black box. no need to understand anything
2026-10-19 17:59:26
35
westdevx86
westdevx86 :
Holy crap this just helped me understand SO many linear algebra concepts that didn't make sense to me. Like I never really understood the SVD and eigen values/vectors that well until watching this video
2026-10-20 16:59:37
0
dmeurpcyh83
𝔈𝔦𝔡𝔯𝔢𝔳𝔢𝔫 :
My brain just melted but ts sounds cool asf
2026-10-19 19:33:33
37
its_almost_engineering
almost engineering :
it would be very funny if you purposefully chose those numbers in the beginning, knowint they would have a maximum Eigenvalue of 6,7
2026-10-20 15:28:22
3
nullwristmotion
nullwristmotion :
I don’t have anything to add but Grace Hopper is goated
2026-10-20 06:20:46
2
frank_welter
Frank Welter :
Very impressive explanation, in fact the first I understood.
2026-10-20 01:54:44
5
hankcazorp
Hank Cazorp :
And this is why Netflix offers you a million things that are not quite what you want to watch right now
2026-10-20 01:17:05
9
nopenopenopeeee3
user4324937631476 :
i’ve watched everything
2026-10-19 22:55:37
4
lav.davka
Grilled Cheese :
Symmetric matrices our beloved. Feels like yesterday that we proved in first year of undergrad that the eigenvalues of Hermitian matrices are real and the eigenvectors with different eigenvalues are orthogonal, thus if M is nxn and has n distinct eigenvalues then there exists an orthonormal basis of eigenvectors. The Spectral Theorem is my favourite in the whole of mathematics.
2026-10-19 20:31:18
16
milekragulj
Mile Kragulj :
Grace Hopper. Creator of tha first program language. Admiral.
2026-10-20 04:35:04
1
_salvatore_502
_Salvatore_ :
bruhhh we need u on YouTube
2026-10-20 14:07:50
0
d610155
d :
ah yes, fiml
2026-10-20 02:39:47
0
2degreesummit
Tommy :
Is the eigenvalue decomposition mentioned just the diagonalization of A?
2026-10-20 00:47:11
1
hironohero
Hironohero :
Coco mentioned 🙌
2026-10-19 22:48:02
0
its_almost_engineering
almost engineering :
wait, is that the k-value for LLMs? the approximation? top-k
2026-10-20 15:34:29
3
cathalmcstay
Cathal McStay :
Everywhere I go, I see a Grace Hopper
2026-10-19 22:57:28
0
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