Thank you so much for posting these! I love that you say you owe "us" an explanation or example - most professors and the book don't and just keep going, so I really, really appreciate your explanations! Thank you from a math student that's not in your class haha
This is great review for my Lin Alg midterm coming up. Giving me hope. I can do this. Thank you for making this accessible and clear. You are saving my will to push through difficult times.
hi, im a little late but in the first example, at 9:38 you say that b is a scalar. In the question, the set forms a subspace iff b=0, are we talking about the scalar 0 or the vector 0? I'm a little confused
Dear professor, are there homeworks available for outside student ( not UW student) like me to work while learning from your video lectures? Btw, Thank you for your lectures video, It is great to find abstract linear algebra lecture on youtube!
Hi Huy. Glad you're getting something out of them! Send me an e-mail (click the link to my website in the description to find it) and I can send you the homework for the class.
@@ProfWonMath I will send you email soon!. Btw, i see that many courses in abstract linear algebra teach Jordan form, but i dont see it in your lectures :(((
Professor Won, how can I get access to the homework’s? I’m watching the lectures and I really like them so I want to understand the materials deeply. Thank you for uploading the lectures. Btw, the link in the description isn’t working.
may I ask why is so important that each vector in the Direct sum must have a unique rappresentation? is this just a definition or there's a deeper meaning behinde this?
The notion of "every vector in V can be written as a sum of vectors in the subspaces U and W, but the representation is not unique" just corresponds to the notion of the *sum* of subspaces. In that case, you might write V = U + W. However, this does not tell you as much about V. For example, it is trivial that V = V + V. But writing V as V + V does not really tell you how V decomposes into two subspaces. It is more useful to note that V = V + {0}, which is a direct sum.
You might also notice the similarity to the property of a basis (where every vector in V can be written as a linear combination of the basis vectors, and also this linear combination is unique). This corresponds to the fact that if V is the direct sum of U and W, you can get a basis of V by taking the union of a basis of U and a basis of W. If V is just the sum of U and W, then if you take a union of the two bases, you will only get a spanning set, in general.
Thank you for posting these! Does anyone know of a resource that explains how R^[0,1] is the set of all functions [0,1] → R? It's nowhere in the book, and because the book introduces R, I'm not sure how I was supposed to know this property of it. It's possible that this is a basic notation from another field that I just never learned; if so, what is it so that I can learn it first?
Axler introduces it in example 1.24. It is somewhat standard (see the first example in en.wikipedia.org/wiki/Function_space) but not so standard that I think it can be used in any context without explanation.
![The most beautiful equation in math, explained visually [Euler’s Formula]](/img/n.gif)
Thank you for this. I really appreciate how you incorporate exercises throughout the lecture. It keeps things engaging.
Thank you so much for posting these! I love that you say you owe "us" an explanation or example - most professors and the book don't and just keep going, so I really, really appreciate your explanations! Thank you from a math student that's not in your class haha
don't know where I would be without you😊cant thank you enough
This is great review for my Lin Alg midterm coming up. Giving me hope. I can do this. Thank you for making this accessible and clear. You are saving my will to push through difficult times.
love the vids, but i just wish you could clarify u and U more, as they usually look the same.
Prof, I find your videos very helpful. Where can I find the first two videos, 1A & 1B?
It's been posted!
hi, im a little late but in the first example, at 9:38 you say that b is a scalar. In the question, the set forms a subspace iff b=0, are we talking about the scalar 0 or the vector 0? I'm a little confused
Dear professor, are there homeworks available for outside student ( not UW student) like me to work while learning from your video lectures? Btw, Thank you for your lectures video, It is great to find abstract linear algebra lecture on youtube!
Hi Huy. Glad you're getting something out of them! Send me an e-mail (click the link to my website in the description to find it) and I can send you the homework for the class.
@@ProfWonMath I will send you email soon!. Btw, i see that many courses in abstract linear algebra teach Jordan form, but i dont see it in your lectures :(((
huy, could you please foward the homework to me?
Where is 1.A and 1.B?
It's now been posted!
Professor Won, how can I get access to the homework’s? I’m watching the lectures and I really like them so I want to understand the materials deeply. Thank you for uploading the lectures. Btw, the link in the description isn’t working.
Same
@@bobjjinag7323 Send me an e-mail (you can find it by Googling me)
Send me an e-mail (you can find it by Googling me)
Wow, I can see why this is such a popular video!
may I ask why is so important that each vector in the Direct sum must have a unique rappresentation? is this just a definition or there's a deeper meaning behinde this?
The notion of "every vector in V can be written as a sum of vectors in the subspaces U and W, but the representation is not unique" just corresponds to the notion of the *sum* of subspaces. In that case, you might write V = U + W.
However, this does not tell you as much about V. For example, it is trivial that V = V + V. But writing V as V + V does not really tell you how V decomposes into two subspaces. It is more useful to note that V = V + {0}, which is a direct sum.
You might also notice the similarity to the property of a basis (where every vector in V can be written as a linear combination of the basis vectors, and also this linear combination is unique). This corresponds to the fact that if V is the direct sum of U and W, you can get a basis of V by taking the union of a basis of U and a basis of W.
If V is just the sum of U and W, then if you take a union of the two bases, you will only get a spanning set, in general.
@@ProfWonMathohh many thanks 🙏
Thank you for posting these! Does anyone know of a resource that explains how R^[0,1] is the set of all functions [0,1] → R? It's nowhere in the book, and because the book introduces R, I'm not sure how I was supposed to know this property of it. It's possible that this is a basic notation from another field that I just never learned; if so, what is it so that I can learn it first?
Axler introduces it in example 1.24. It is somewhat standard (see the first example in en.wikipedia.org/wiki/Function_space) but not so standard that I think it can be used in any context without explanation.
@@ProfWonMath I have no idea how I missed that! Thanks so much for the reply ✨
Having the letters DR as a prefix to the name does not mean that one is a Physician!!! The Physician has the letter MD as a suffix after the name!!!