6. Singular Value Decomposition (SVD)

MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Instructor: Gilbert Strang

Singular Value Decomposition (SVD) is the primary topic of this lecture. Professor Strang explains and illustrates how the SVD separates a matrix into rank one pieces, and that those pieces come in order of importance.

License: Creative Commons BY-NC-SA

[tetrabromobisphenol]

Gilbert Strang is a treasure to the world. His books are top notch, and the MIT Open Courseware has made it possible for myself and so many others to learn at our own pace. Many thanks Dr. Strang!

[indrajitjana]

Thumbs up to the camera angle management team; great video audio editing.

[saitaro]

His explanations have always been impeccable. What a legend.

[gzitterspiller]

I love the way he always explains everything from the beginning, he tells you the whole process.

[nishantraj]

One of the best lectures on Youtube, thanks Prof. Gilbert for explaining this beautifully.

[FranekMag]

Fantastic lecture, really appreciate MIT sharing the course lectures for free.

[dalisabe]

Awesome! I could watch the lectures over and over and each time, I gain a different and extra insight into the results and the process. Linear Algebra could turn into magic after you apply it’s theory—-the once dull computations of rows and columns. The most fascinating aspect of linear Algebra is when the entire matrix details unfold into a single effect, one that resembles the effect of simple scalars used in simple math formulas. Thanks to the fundamental concept of the Eigenvectors and Eigenvalues. Understanding the very essence of a matrix and what it does to any vector quantity (change in magnitude and direction) is the key concept to appreciating the underlying concept of various matrix decompositions. It all boils down to how many ways we could see the workings of a matrix in terms of its decomposed forms. The SVD composition is one of those decompositions of a matrix that allows a matrix to be seen as a sequential transformation of direction and magnitude in terms of some orthonormal basis characteristic of such matrix and its Eigenspace. Such a beauty!

[mauriceli]

love Prof Strang's lecture, enlighten me on the depth of linear algebra

[melisaalkan]

"The key is that A transpose A is a great matrix" :D simply GOAT!

[cpaniaguam]

This SVD business is truly poetry in motion.

[akshayshrivastava]

Thank you very much Dr. Strang for making this intuitive and natural. I had only gone through SVD in bits and pieces and never had what I could consider a good enough understanding until I saw this lecture.

[youngjim]

He just saved my from the brim of breaking down trying to understand SVD! What he presented is so natural, so beautiful that I instantly catch them. Appreciate MIT open courseware also!

[clecarosc]

This is pure gold... such a fantastic Professor!! Thank you

[megh]

Genius of this Man is the way he is explaining such a difficult concept so Hatts Off. As per Indian Ethos I just want to touch your feet.

[gyeongchankim]

This lecture in specific was truly beautiful

[lfalfa]

God bless your existence, Prof. Strang.

[Hank-rybz]

16:23 symmetry; 28:50 geometry; 42:24 "econ" SVD

[vigneshbhaskaran]

This lecture singularly helped me through the concepts on use of eigen values for capturing variability

[BigBen]

I am confident once I went through a Refresher up to this point that his explanation will be as clear as water😀 Because none of my advanced mathematics professors ever explained in such detail!! Awesome professor 👍🏾🙏

[wxie]

Prof Strang is mathematical elegant in delivering linear algebra in an understandable way