Cool pencils for vectors! I suppose we assume that villages in the example are on the plane surface, not in the mountains. Otherwise on a round planet traveling from one town to the town on the other side of the planet could really be a curve and the straight vector would be similar to a tunel throgh the Earth. O well, people drill tunels in the mountains too.
0:11 : Mathematics in a disciplined way 0:56 : commutativity 3:33 : associativity 8:34 : Important Note (associativity as being more fundamental than commutativity) 9:44 : distributivity 13:50 : Important Note (these 3 properties are absolutely essential to LA)
One advice. Add some description for these videos. You have really good presentations and they are not trivial and common on the internet, but to find them.... noooo.. For this particular video it would be nice to have title "intuition behind assosiativity, commutativity and ect."
Outstanding. You explain every detail sufficiently, without making leaps a novice couldn't follow. At the same time you don't linger on topics until the viewer's attention fades or they start to forget earlier parts of the lecture (and possibly its context) - my biggest gripe with _Khan Academy_. I really hope I can follow this course through, unfortunately lacking talent in mathematics.
You could have explained the distributivity in your diagram with the help of similarity... As the direction of vector b is same, the smaller triangle and bigger one are similar to each other and hence the ratio of corresponding sides are to be same
Hello, I plan to take your course once the Lemma system is developed. I have watched some videos so far. Looks good and thanks for making this. The reason I want to learn Linear Algebra is because it's a requirement for Machine Learning. I also heard that Linear Algebra goes hand in hand with Differential Equations. My Question is, do you also cover Differential Equations? It will be nice to knock both topics in one course. Once again, thanks for this.
Exponentiation is not-associative , (a^b)^c =/= a^ (b^c) This is clearer if we use function notation. Define f(a,b) = a^b Then (a^b)^c = ( f(a,b) ) ^c = f ( f(a,b), c) and a^(b^c) = f(a, b^c) = f( a , f(b,c) ) .
Prof, I think you can be even more convincing in the distribution proof by invoking similar triangles OA/OA'=AB/A'B'= OB/OB' (labelling the old tips A & B and the new tips A' & B').
Don't talk like that about Wikipedia =( It's a generally good website!!! For example, this article right here is great & high quality: en.wikipedia.org/wiki/Earth
Outstanding. You explain every detail sufficiently, without making leaps a novice couldn't follow. At the same time you don't linger on topics until the viewer's attention fades or they start to forget earlier parts of the lecture (and possibly its context) - my biggest gripe with _Khan Academy_. I really hope I can follow this course through, unfortunately lacking talent in mathematics.
Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.
I was seriously watching untill messi popped up. Youre a very good teacher. Thanks :)
This is what it means to be a very good teacher. Thank you
Thank you. You do an amazing job of clarifying this subject. Special thanks for not wrapping the big picture in fatiguing notation.
+Drawer Thanks. Make sure to also check out Gil Strang's videos on linear algebra.
+MathTheBeautiful I have and he loses me about halfway through the subject. I hope it doesn't happen here.
+Drawer I'm sure you'll back to it in the future and it'll make sense.
Cool pencils for vectors! I suppose we assume that villages in the example are on the plane surface, not in the mountains. Otherwise on a round planet traveling from one town to the town on the other side of the planet could really be a curve and the straight vector would be similar to a tunel throgh the Earth. O well, people drill tunels in the mountains too.
That Messi picture caught me off guard lol
I was looking for this comment lol
0:11 : Mathematics in a disciplined way
0:56 : commutativity
3:33 : associativity
8:34 : Important Note (associativity as being more fundamental than commutativity)
9:44 : distributivity
13:50 : Important Note (these 3 properties are absolutely essential to LA)
6:35 : Messi
Thanks a lot for these videos. So good teaching, I can't stop watching!
One advice. Add some description for these videos. You have really good presentations and they are not trivial and common on the internet, but to find them.... noooo..
For this particular video it would be nice to have title "intuition behind assosiativity, commutativity and ect."
Outstanding. You explain every detail sufficiently, without making leaps a novice couldn't follow. At the same time you don't linger on topics until the viewer's attention fades or they start to forget earlier parts of the lecture (and possibly its context) - my biggest gripe with _Khan Academy_. I really hope I can follow this course through, unfortunately lacking talent in mathematics.
Such a great teacher, thanks a lot sir
You could have explained the distributivity in your diagram with the help of similarity... As the direction of vector b is same, the smaller triangle and bigger one are similar to each other and hence the ratio of corresponding sides are to be same
Hello, I plan to take your course once the Lemma system is developed. I have watched some videos so far. Looks good and thanks for making this.
The reason I want to learn Linear Algebra is because it's a requirement for Machine Learning. I also heard that Linear Algebra goes hand in hand with Differential Equations. My Question is, do you also cover Differential Equations? It will be nice to knock both topics in one course.
Once again, thanks for this.
Sure, differential equations (at least the part that 99% of us need to know) are a brief footnote to linear algebra and the topic of eigenvalues.
Were you too reading the Book "Mathematics for Machine Learning" by Marc Deisenroth that recommended this channel?
What is with the soccer photo at 6:35?
LOL Messi is a soccer player :P
The drawing starts getting a little bit messie
Thank you , you convinced me very good
Exponentiation is not-associative , (a^b)^c =/= a^ (b^c)
This is clearer if we use function notation.
Define f(a,b) = a^b
Then (a^b)^c = ( f(a,b) ) ^c = f ( f(a,b), c)
and a^(b^c) = f(a, b^c) = f( a , f(b,c) ) .
That's a great example of non-associativity. I've never thought of it before.
what about c+ (a+b) in associativity?
Isn't that just commutativity you're showing?
Prof, I think you can be even more convincing in the distribution proof by invoking similar triangles OA/OA'=AB/A'B'= OB/OB' (labelling the old tips A & B and the new tips A' & B').
Wow! Is that a real CHALKBOARD and real CHALK? I haven' t seen those in years! 😊 Great lesson! Thanks!
ruclips.net/video/W3s04J3I6Sw/видео.html
"beautiful" presentation
6:34
Take a bow!!
trippy :D
than
You're welcome!
Don't talk like that about Wikipedia =(
It's a generally good website!!! For example, this article right here is great & high quality:
en.wikipedia.org/wiki/Earth
Messi 🤣
Outstanding. You explain every detail sufficiently, without making leaps a novice couldn't follow. At the same time you don't linger on topics until the viewer's attention fades or they start to forget earlier parts of the lecture (and possibly its context) - my biggest gripe with _Khan Academy_. I really hope I can follow this course through, unfortunately lacking talent in mathematics.