Wonderful to have you back... Still keep your excellent book on Tensor Analysis & The Calculus of Moving Surfaces on my desk... Strange and Grinfeld: Great Books and lectures to learn by...
Professor, please continue making videos regularly. I absolutely love your lecture series and books. Your book on Tensor Calculus is amazing. And thank you for making this particular lecture available online. If there is one math book which I like more than yours, its by Prof Strang. You two have an amazing command over these critical subjects.
Hello back professor Grinfeld, you're Linear Algebra playlist the the True One and I've learned so much so far, now I'm addicted to your teaching approach for math. Wished you had a calculus1 playlist too. Sheers
Professor, kindly make a series on ordinary differential equations as well. It will be great to re learn the subject using your insights on the topics. Thank you.
I've tried first with professor Strang. I watched the first video of his playlist and I learned quite goo. Then the second, and I didn't know what was going on. Only with Dr Grinfeld playlist I truly learned the essence of Linear Algebra. From totally beginner to enjoy LA. I don't know how did you learn from Strang. Maybe in engineering way? Could you tell more?
Hello professor Grinfeld.! Have you ever thought of creating a calculus playlist for beginners, as your Linear Algebra playlist? It would be phenomenal for people like myself, whom\who enjoy math and want to become mathematicians.
I also wish professor Grinfeld creating a calculus playlist. Professor Grinfeld's Linear Algebra playlist is the course make me become confident with Linear Algebra(I went through several others before). Your insight in the field helps me understand more deeply.
Hi professor, 1) At first perform Gram Schmidt on the columns and throw away dependent columns which are mapped to 0 by the GS algorithm. The orthogonal vectors are then discarded after they did the job of throwing away the dependent columns. This process reaches the C matrix. 2) Derive the coefficient of the linear combination that yield the dependent columns. For some applications, taking the orthogonal columns in (1) and not throwing them away in favor of the original independent columns, may be more attractive, especially in Machine Learning.
Hi Eytan, I like the idea of using GS to eliminate the linearly dependent vectors, as it injects the discussion with geometric ideas. However, I think it's less efficient. Also, the Strang decomposition is "affine", i.e. it does not require the notion of an inner product. Meanwhile, GS needs an inner product.
@@MathTheBeautiful Inner product exits both in the C and in the R fields. From my experience, it is a numerically highly efficient process unless the column vectors are nearly parallel. In ML applications a near representation is sufficient. If after normalization, the removal of projections on previous columns leaves a small norm, the new column is not normalized buy discarded even if its norm is not zero. A threshold on the norm is defined before the process starts. A representation which is nearly perfect is desirable in Machine Learning.
No offense but "how useful is it" is about the dumbest question I've ever heard asked in a math class, hands down. Followed by "Who's {the first name of the author of the method}?" What a knee slapper. 🤣
Wonderful to have you back... Still keep your excellent book on Tensor Analysis & The Calculus of Moving Surfaces on my desk... Strange and Grinfeld: Great Books and lectures to learn by...
Your back! Thank you so much for this upload.
Professor, please continue making videos regularly. I absolutely love your lecture series and books. Your book on Tensor Calculus is amazing. And thank you for making this particular lecture available online. If there is one math book which I like more than yours, its by Prof Strang. You two have an amazing command over these critical subjects.
Dr Grinfeld studied under Strang at MIT :)
@@benstear581 and it shows. Both are just amazing! But then, Dr PGs use of R as column space is a massive offense!
Thank you, mr. Strang's intellectual heir.
I appreciate the emphasis on beauty and aesthetics in these formulas. They help make mathematics less dry and more beautiful.
Hello back professor Grinfeld, you're Linear Algebra playlist the the True One and I've learned so much so far, now I'm addicted to your teaching approach for math. Wished you had a calculus1 playlist too. Sheers
you are one of my favorite math teachers on youtube i would definitely be lost trying to study math after college without your work
Professor, kindly make a series on ordinary differential equations as well. It will be great to re learn the subject using your insights on the topics. Thank you.
Thank you for being back, with new style, so to say.
thank you for your persistence
Must be very cool for those kids to have Seth Rogen as their math professor.
Personality or weight?
Nice presentation. I learnt alot
Great video! Welcome back!
YAAAAAS! NEW VIDYA! LESS GO! MathTheUploader!
„Let me dive right into it…“ is at 11:16
Thank you so much, you saved me 6 minutes of fluff :)
Yep! Professor Gilbert Strang is the main go-to person for anything Linear Algebra.
lol
I've tried first with professor Strang. I watched the first video of his playlist and I learned quite goo. Then the second, and I didn't know what was going on. Only with Dr Grinfeld playlist I truly learned the essence of Linear Algebra. From totally beginner to enjoy LA. I don't know how did you learn from Strang. Maybe in engineering way? Could you tell more?
@aDBo'Ch 1 The 'Albert' was used for fun. As an allusion to Einstein. But this one is Gilbert.
And he is back
Lovely! Thank you so much
That is a very Strang[e] decomposition :)
What he said is portable as potentially portraiture of dancers in flying.
Welcome back !!!
Are you telling me I should’ve learned this but didn’t? It’s very nice
Well, it didn't exist so no regrets!
Hello professor Grinfeld.! Have you ever thought of creating a calculus playlist for beginners, as your Linear Algebra playlist? It would be phenomenal for people like myself, whom\who enjoy math and want to become mathematicians.
I also wish professor Grinfeld creating a calculus playlist. Professor Grinfeld's Linear Algebra playlist is the course make me become confident with Linear Algebra(I went through several others before). Your insight in the field helps me understand more deeply.
the statement about algebra is so true
How to do this CR decomposition in Matlab ?
I'm certain I've used this many times before without realizing it has a merit on its own.
Yes, that's the brilliance of it!
Sir, will you make videos on the Applications of Linear Algebra...like Data Science field etc...
Hi professor, 1) At first perform Gram Schmidt on the columns and throw away dependent columns which are mapped to 0 by the GS algorithm. The orthogonal vectors are then discarded after they did the job of throwing away the dependent columns. This process reaches the C matrix. 2) Derive the coefficient of the linear combination that yield the dependent columns. For some applications, taking the orthogonal columns in (1) and not throwing them away in favor of the original independent columns, may be more attractive, especially in Machine Learning.
Hi Eytan, I like the idea of using GS to eliminate the linearly dependent vectors, as it injects the discussion with geometric ideas. However, I think it's less efficient. Also, the Strang decomposition is "affine", i.e. it does not require the notion of an inner product. Meanwhile, GS needs an inner product.
@@MathTheBeautiful Inner product exits both in the C and in the R fields. From my experience, it is a numerically highly efficient process unless the column vectors are nearly parallel. In ML applications a near representation is sufficient. If after normalization, the removal of projections on previous columns leaves a small norm, the new column is not normalized buy discarded even if its norm is not zero. A threshold on the norm is defined before the process starts. A representation which is nearly perfect is desirable in Machine Learning.
Gilbert Strang's video on CR factorization: ruclips.net/video/BFYU9wywgtY/видео.html
How can I find that decomposition on the internet?
strang
Indeed!
His outfit matches the color of the chalk board...
cool
orange juice
Give him some bongos. I’ll even join in with an alto sax to add some quantum math to it!
I didn't dn't understand a shit! But was really interesting 😂😂
Video actually starts at 11:13. You're welcome.
I respectfully disagree :)
No offense but "how useful is it" is about the dumbest question I've ever heard asked in a math class, hands down. Followed by "Who's {the first name of the author of the method}?" What a knee slapper. 🤣
None taken