This video was surprisingly easy to follow. Its been years since I have done anything involving Linear Algebra but I was able to follow the video thoroughly.
Feedback: It would be really helpful if you could add (for those who require it), that an inner product requires conjugate symmetry. It just so happens that if you’re dealing with real fields then conjugate symmtery becomes your normal symmetry. I believe these small sidenotes would help point people, who are looking for more advanced linear algebra concepts, in the right direction. It would also make it easier for people to make connections between what’s presented here, and what is popularly found online. (i.e: Wikipedia)
Followed and understood everything for a system technician. This dude explanation is top notch 🎉🎉🎉 i can imagine how good he would be if he used visual software🎉🎉🎉. Any recommended textbooks would be appreciated. Subs and liked
What I don't like about inner product spaces is the name. I think important mathematical concepts ought to have short names. For example, vector spaces with a norm are called normed spaces. This is short and sweet. Inner products and their variants are so ubiquitous that they really ought to have a more concise and compact name. Also, I think names should be explained. What is 'inner' about inner product spaces? And does this mean there is also an outer product in contrast? And if so, how do they relate? I've seen certain specialisations of the tensor product called outer products. So I guess that answers one of my questions. And I expect its called 'inner' because it reduces the 'dimension' of the product - from a vector to a scalar. Whilst an 'outer' product increases the dimension, from a pair of vectors to a 2-vector. What I'm driving at here is that maths has a history thats embedded in its notation amd naming strategy. And I think that its worth making explicit. My suggestion for an alternative name for an inner product space is one thats imported from physics - a metric. Thus a metric space. Unfortunately this clashes with the standard notion of a metric space in maths. I guess we could distinguish the former from the latter by calling the former, a metric vector space and the latter, a topological metric space. And my vote for the most awkward name in maths goes to sesquilinear form. This, is a bilinear form that is linear in one variable and conjugate linear in the other. Since this comes up all the time for vector spaces over the complex numbers, we ought to have a nicer name for this too.
Maths. Because maths can exist without science and even the number 1 can be classified as maths and started in the time of cavemen before people could talk
Since I am building a perpetual motion machine that Gottfried Leibniz watched run for 2 hours, when he published his work, was Newton correct when Newton said it was his own work? Did Leibniz learn of Newton's unpublished work which only Newton's friends knew of? Because I am 1/2 Norwegian I basically learned to talk in Norway. Bessler was 1/2 Polish and Leibniz was a witness for Bessler when Bessler was arrested for being a fraud. Bessler wasn't convicted. To be a jerk I'll show how Newton could've used his math to show why the Moon orbits the Earth. Johannes Keppler used the inverse square law to understand the motion of the planets around the Sun. If Newton would've been tolerant of Keppler then he would've been a genius. I just explained Newton's most famous work. I think everyone will miss what I just said. It's not like the letter that Newton wrote to Keppler but is much more direct. Nothing personal Tom but people need to understand that science and math like anything else involves mind games and politics.
