Complex Matrices ( An intuitive visualization )

[@amansawarnaya4329]

Awesome explanition sir . Found this video amazing ❤

[@rishitpurbey2714]

Well explained, good work!

[@nidhikulkarni6902]

You've explained it so well, sir! Love your interpretation! Thank you, sir! 🙌✨

[@hardikgrover7883]

Great animations, well explained👌👍👍

[@devilishhdj1871]

Amazing video!! Thank you

[@AWESOMEEVERYDAY101]

Glad u enjoyed it ^^

[@_Prajval]

Awesome Explanation Sir 👌🏻

[@1495978707]

5:55 This order of writing vector and matrix is opposite of what has been standard for like 100 years

[@AWESOMEEVERYDAY101]

I realised that after the video had be completed. Hope it's not too much of a problem!

[@宋雅楠]

It baffled me too

[@jaykane42]

Sorry, I don't fully understand why we can't multiply v with R right off the bat at 15:25. I might just be being stupid or have missed something earlier in linear algebra - in which case I apologise. If not, please, would you mind explaining why we can't multiply it? Thanks! Also, this video has helped me a lot!

[@jaykane42]

If you are confused as to what I don't understand. It's that I don't understand what it not being commutative has to do with anything. Why can't we just do it one way? or, does neither way work and if so, why? Sorry if I'm asking too many questions

[@AWESOMEEVERYDAY101]

Sorry for the delay, We can't multiply v with R instantly is because it doesn't give a hermitian matrix which describes a vector. The commutativity I described was just a path way to thinking about rotations that didn't work. For example if we had only talked about R and v it would be a logical assumption that "vR or Rv should do the proper rotation but which one?" but this doesn't work either way. The base topic on which complex matrices are based on ("based on" in the context of the video) is Geometric Algebra, and in Geometric Algebra the multiplication leads to a trivector ( ordered/signed volume ) component along with the rotation. So we avoid this by multiplying on both sides of the vector and because we are multiplying with the inverse on one side, the trivectors formed are of opposite sign and in effect cancle out. My purpose of the video was to explain how should we intuitively think about and visualize complex matrices so I didn't go into detail about geometric algebra.

[@agrajyadav2951]

ur awesome dude!

[@haydebre]

It's very illustrative.

[@AWESOMEEVERYDAY101]

Thanks!

[@vikasbisht8903]

Really good sir

[@agrajyadav2951]

at 5:40 you wrote the vector first and then the matrix, which in standard notation is mathematically incorrect as the system becomes incapable of multiplication. Just a small typo prolly, otherwise great video!

[@AWESOMEEVERYDAY101]

Thank you! I realised my mistake pretty late so the video had already been posted. Ty for pointing it out :D

[@angeldude101]

Why would you have to convert to a matrix when you can do the math entirely in terms of yz, zx, and xy? The role of i is also very close to the value xyz, which appears to be a volume.

[@AWESOMEEVERYDAY101]

Yes we can solve everything in xy, yz, zx and xyz but my goal was to get an idea of what complex matrices represent. In geometric algebra we do use xy, yz, zx and xyz and this is equivalent to that, so u can say that 2x2 complex matrix is a way to represent trivectors, bivectors and vectors in 3D. Explaining geometric algebra would have derailed the topic. Also depending on the context different notations are helpful. The xyz is a "signed volume" or a "directed volume" and in 3D it behaves as the complex number i. This is explained in more detail in Geometric algebra. Hope this helps ^^

[@angeldude101]

@@AWESOMEEVERYDAY101 Ah so you do know. 😉

[@TheJara123]

Cool man, thanks..more math...

[@AWESOMEEVERYDAY101]

Np hope u liked the vid.