Hi, I came here from the SoME2 judging, and you have a very interesting video. I can tell that both of you know what you are talking about and are passionate about math. Definitely earned my subscription!😁
Your explanation of the connection between graphs and their matrices was very good! However, you frame Kirchhoff's law as the main result of your discussion without being explicit near the end about how the incidence matrix encodes the sum of voltages along a path of edges. While still hinted at in the main discussion, this makes the loop law seem to appear out of nowhere. You're video is great, but your recap could have been oriented toward summarizing your discussion in light of your circuit representation. This would have clarified the result.
Hi-Akshay here! Yeah, I totally agree. We should have included the final bridge between voltage and the incidence matrix operator. Thanks for taking the time to watch our video and give feedback!
A clear exposition. More Linear Algebra and Graph Theory, please. Everything is a graph, but there is a higher level graph in which the graphs here are just nodes there, with the higher level edges connecting and disconnecting dynamically from the nodes of our level, based on bias, since direct connection would collapse things into the lower level graph. The bias is provided by feedback from the lower level. Which explains a Lot.
Interesting video, thank you! One thought that occurred to me while watching was that you could've saved approx. 10 minutes by linking to 3blue1brown's "essence of linear algebra" -playlist (from 9:40 to 19:45).
I really liked this! I can't believe I just found your channel - as a video creator myself, I understand how much time this must have taken. Liked and subscribed 💛
Feedback: Circuit in physics is not the same as circuit in graph theory. So you cannot say it is a math topic in the beginning. Other than this, the flow is quite smooth, and the topic is quite interesting. Also the presentation about the relationship between graph and its matrix is very clean and clear. Further reading: R. J. Wilson, Introduction to Graph Theory; J. Clark and D.A. Holton, A First Look at Graph Theory
Hi, Akshay here! I agree-the vocab can be confusing. Our logic was that because we never use the term "circuit" in the graph sense, it was safe to call the electrical schematics "circuits." Thanks for the resources and taking the time to watch the video and give feedback!
I'm a bit confused how null space determines cycles. I would think that adding extraneous edges to a Directed Acyclic graph would cause null spaces, wouldn't it? I think it should be possible to add these while introducing no new cycles. Is there a flaw with my reasoning?
I don't understand, how the voltage change got into this, we haven't even introduced it. The (incidence).(edges of a cycle) = 0 just means that in each vertex #incoming-#outgoing edges of the cycle is 0, which kind of looks similar to the currents law (not voltage), but the implication seems to me in the opposite direction: since the charge doesn't accumulate in vertices, the current is in the span of the null space and hence can be presented as a combination of circular currents. Could you clarify all this please?
You're absolutely right-we originally had a bit of the script dedicated to the connection, but we forgot to animate it so it didn't get into the video.
Hi, I came here from the SoME2 judging, and you have a very interesting video. I can tell that both of you know what you are talking about and are passionate about math. Definitely earned my subscription!😁
Glad to hear it! Expect a video 1 year from now for SoME3!
I have noticed this connection when I was undergraduated.
I used Modified Nodal Analysis to solve linear circuits.
Your explanation of the connection between graphs and their matrices was very good! However, you frame Kirchhoff's law as the main result of your discussion without being explicit near the end about how the incidence matrix encodes the sum of voltages along a path of edges. While still hinted at in the main discussion, this makes the loop law seem to appear out of nowhere. You're video is great, but your recap could have been oriented toward summarizing your discussion in light of your circuit representation. This would have clarified the result.
Hi-Akshay here! Yeah, I totally agree. We should have included the final bridge between voltage and the incidence matrix operator. Thanks for taking the time to watch our video and give feedback!
There are many excellent videos chasing Kirchhoff’s Law. In many interesting ways. It is highly interesting.
A clear exposition. More Linear Algebra and Graph Theory, please. Everything is a graph, but there is a higher level graph in which the graphs here are just nodes there, with the higher level edges connecting and disconnecting dynamically from the nodes of our level, based on bias, since direct connection would collapse things into the lower level graph. The bias is provided by feedback from the lower level. Which explains a Lot.
Oh, and some regular math. I need a refresher so I can work on this. My freshman college math is sixty years old.
What a brilliant derivation of Kirchoffs law!
fax my brother! spit your shit indeed!
Interesting video, thank you! One thought that occurred to me while watching was that you could've saved approx. 10 minutes by linking to 3blue1brown's "essence of linear algebra" -playlist (from 9:40 to 19:45).
I really liked this! I can't believe I just found your channel - as a video creator myself, I understand how much time this must have taken. Liked and subscribed 💛
Very interesting tutorial ❤
A gem 💎 ! Great revision
man keeping track of all these SoME 2 videos is getting harder. Dont want to leave any unwatched.
well explained! looking forward to your next videos
Brilliant thank you
22:38 I think the example graph actually has 4 cycles: cefbg, cefa, cdbg, cda. Have I missed something? Is there some independence condition perhaps?
I guess because cefa + cdbg = cefbg + cda in the edge vector space, only three of them are linearly independent
interesting video ! Hope you will make more in the future
You bet!
Feedback:
Circuit in physics is not the same as circuit in graph theory. So you cannot say it is a math topic in the beginning. Other than this, the flow is quite smooth, and the topic is quite interesting. Also the presentation about the relationship between graph and its matrix is very clean and clear.
Further reading:
R. J. Wilson, Introduction to Graph Theory;
J. Clark and D.A. Holton, A First Look at Graph Theory
Hi, Akshay here! I agree-the vocab can be confusing. Our logic was that because we never use the term "circuit" in the graph sense, it was safe to call the electrical schematics "circuits." Thanks for the resources and taking the time to watch the video and give feedback!
All the beauty happens at 19:40😊
more videos like this
Very interesting connection!
Simply Brillant!
I'm a bit confused how null space determines cycles. I would think that adding extraneous edges to a Directed Acyclic graph would cause null spaces, wouldn't it? I think it should be possible to add these while introducing no new cycles. Is there a flaw with my reasoning?
This is very nice to offer as an educational tool. Thankyou
There is a recent computerphile video on knowlege bases.should be refered to this one
I don't understand, how the voltage change got into this, we haven't even introduced it. The (incidence).(edges of a cycle) = 0 just means that in each vertex #incoming-#outgoing edges of the cycle is 0, which kind of looks similar to the currents law (not voltage), but the implication seems to me in the opposite direction: since the charge doesn't accumulate in vertices, the current is in the span of the null space and hence can be presented as a combination of circular currents. Could you clarify all this please?
You're absolutely right-we originally had a bit of the script dedicated to the connection, but we forgot to animate it so it didn't get into the video.
Brilliant! We want more!
Interesting thank you
This was flawless!! I really enjoyed it! Great work!
Hello , what do you plan to be your channel about ? Math , Engineering or CS?
I study in the school
pogging
Thank you, Ms. Baguette. Your in-depth feedback is appreciated by Mr. Choi and I.
Fancy
Sorry but I had to immediately stop the video on hearing “Algebra” pronounced with a hard g. What’s up with that?