In the middle of my PhD, with all the stress, Dr. Strang's lectures are the only relaxing time I have. Nothing else really feels so great. What a legend. I wish I could attend his lectures physically.
You should.. uh.. get a guitar or maybe go on a hike or learn to cook a new dish from scratch. Glad to hear Gilbert's lectures are peaceful for you, but the stress of academia can be monumental and debilitating over time. Hobbies outside of academia can save your life. Fishing is a great hobby--lots of time to think about science or whatever you want, but you're exercising, and spending time in nature.. best of luck on your degree!!!
does it make sense that during the middle of my PhD I put everything on hold and binge followed lectures+bookchapters+exercises to once and for all fill the gap in the knowledge in crucial areas in wireless and DL. It is taking time but It feels like time well spent
I've finished this course a while ago. still, going through Markov chains in probability was confusing till I came back and watched this, and again, Mr Strang came to the rescue. I don't know how much I need to thank you for your online courses for it to be enough, as simply saying thank you doesn't do you justice. I just want to say that you, Mr Strang is one of a minority of people who indeed make this world a better place. Thank you, from some corner of this Earth.
This lecture is amazing. Pro.Strang gives an intuitive perspective Fourier Series, and how it is related to orthogonal vector. I know Fourier transform pretty well but now have a deep understanding of that.
my proffesor in signals and systems explained in a single class all the the prequisites for linear algebra leading to fourier series, i can gurantee you not a single person unless he's already mastered linear algebra understood her. This guy is most amazing proffesor ive ever seen, makes complex things really simple@@yuchujian8837
Professor Strang's introduction to projections using Fourier Series as an example generalizes to other orthogonal functions (Legrendre Polynimials, Bessel Functions, etc.). This is pretty cool, because you'll see this stuff ad nauseum in electrodynamics, quantum mechanics and statistical mechanics.
Yes, the collapse of wavefunction is a central concept in Quantum Theory. Measurement can be understood as projection of the wavefunction onto one of the orthonormal basis states i.e., taking the dot product between the wavefunction and a basis state.
My god this is so beautiful. So much insight making things fall into place. "Finding coefficienes in a Fourrier series is exactly like an expansion in an orthonormal basis". Now I get it!
This is the moment in time where I have to say thank you! In my opinion this lecture connects everything that happend until now beautifully and builds the foundation for solving most advanced engineering problems.
Prof. Strang's lectures are legendary 😭I've been following this course for a while and it has been a delight to see the concepts unfold in such an elegant and coherent way
The link between Orthonormal vectors and Trigonometric functions by the example of Fourier Series! Great example with Great connection between Algebra and Function! at 44:00. Thanks!
me too haha. I guess because its somehow related to calculus? or differential equation, if you are not quite familiar with those topics, i guess it might add difficulties to us to see what the lecture is actually trying to prove, and the actual use of these matrix. However, you might probably remember these stuff, when you actually need them in the future. then you can pick up these knowledge again and solve the puzzle hopefully
Ah man, I know that feeling. You get to the end of a lecture and realise that you haven't understood anything for several lectures. It can really be worth it to rewatch carefully.
It is worth pointing out that A in the the notation N(A) (16:00) is a generic reference to matrix, not the Markov matrix used as a concrete example. Clarify this confusion, and we could better understand why the eigenvector of eigenvalue 1 is in the null space of ‘A’.
Professor Strang can almost always explain a concept from an angle other professors rarely touch upon. Excitingly, that angle seems always to be the right angle most appropriate to understand that concept.
Prof. Strang's lectures are legendary 😭I've been following this course for a while and it has been a delight to see the concepts unfold in such an elegant and coherent way
This is certainly God level! Things he is saying at times, not only predicting the answers to himself but also to the audience, just to assure them that they can do it too. Also, not being there predicting and waiting for more than a few more secs., for others to still follow!
The eigenvector calculation around minute 33 confused me until I saw how the zero in row three gives an extra degree of freedom in choosing the vector. The check is to multiply by row 2. A nice trick.
I’m taking 18.06 now but Gilbert Strang resigned just before I took the class. Very very sad. His lectures here are perfect though so I can just watch these in my dorm instead of walking all the way to lecture.
In the Fourier series explanation, I think (1, cos, sin, ...) are not unit vectors, cause inner product of cos and cos is pi, not 1. So, I guess, to be orthonormal basis, we need normalization with 1/pi with cos vector. So, In my understanding, just 'orthogonal basis' is correct term for functions (1, cos, sin, ...) as a basis for set of all possible Fourier series' (a vector space).
My goodness, this is beautiful. The insights given by prof. Strang, especially on Fourier series, are out of this world! Thank you very much four your intuition on these profound topics, they are very valuable.
Prof. Strang, you are truly amazing for even a Ph.D, in terms of your lucid explanation and causal but very deep explanation which encourages thinking more than number crunching! It is really an honor to listen to your lecture!
Hawkings radiation compels us to go in for Blackhole as singularity becomes unsteady flow for a vaporisation in a way supports Einstein's refusal to accept Blackhole as singularity.
I didn't know about Markov matrices, they are very interesting. So all n x n matrices with each entry equal to 1/n are Markov matrices, with eigenvalues 0 and 1 (1 because they are Markov matrices, 0 because their rank is equal to 1).
The invention and development of Google is due to Markov Matrices. The things that we see and use everyday in our lives is built on mathematical theory and concepts.
