Annihilator

In this video, I define the notion of an annihilator of a subspace W, and show a neat identity relating the dimension of W and of its annihilator. This should be very reminiscent of the rank-nullity theorem. In a future video (see below), I show why it's useful by showing an amazing corollary. Enjoy!
Amazing corollary: • Rank A^T = Rank A (will be available on 07/15)
Check out my dual spaces playlist: • Dual Space
Subscribe to my channel: / drpeyam

[@Vampianist3]

It starts to become a bit scary that your new videos always appear exactly when I need them - just two days ago I was discussing with my colleagues how annihilators work

[@abbeleon]

Annihilators really sold me on dual spaces and dual bases. Thank you for exploring this topic so clearly!

[@kevinpang4354]

Thank you very much!!!!!!!!! It is the question on my final exam, and I watched this video before.

[@theproofessayist8441]

I heard kernels of vector spaces and annhilators of “modules” are sometimes the same thing. A stackexchange post said annhilators are more general since kernels only work under homomorphisms. Is that correct? Could you please explain why that’s the case - if you need to do it on a separate video that is fine. Would love to see abstract algebra playlist from you if possible Dr. Peyam. Please have a nice day.

[@rigorless6330]

man, if learning linear algebra requires these sorts of mental gymnastics, i cant imagine what teaching linear algebra is like

[@drpeyam]

Awwwww, thanks! It’s a lot of fun though 😄

[@rigorless6330]

@@drpeyam I still managed to follow this video, but I had to rewatch several parts. I got caught up for awhile cuz i thought you said W was a subset not a subspace. I think I'm starting to get the hang of these abstract vector spaces tho!

[@fireemblem2770]

Dr Peyam killing it with the memes!!

[@1memo1717]

Thank you for your effort to explain important topics in maths. It would be much useful if you could try to show the deep insight of the topic you are explaining. This is more challenging. Good luck

[@drpeyam]

But that’s precisely I am doing! Please check out my whole playlist

[@laranoronha591]

thanks doccy p

[@imgayasheck595]

When does Dr. Peyam find the time to keep up with memes? 😂
Can you do a video on summability of divergent series?

[@trewq398]

that would be super interesting

[@rishabhbhutani5835]

Can you please do a video on the double annihilator? By the way, great video!

[@drpeyam]

Maybe, but check out the playlist

[@rishabhbhutani5835]

@@drpeyam I already did, it's great

[@michaelchristinarichardson9660]

Hello master yoda! Can you tell me which text you’re using for this level? Thank you for being so fantastic! ❤

[@drpeyam]

Friedberg Insel and Spence

[@michaelchristinarichardson9660]

Thank you!!! I wish I could come study with you. You are breathing the life into the subject for me. We need more people like you in the departments across our country. I have so much respect and gratitude for you!

[@drpeyam]

Thanks so much 😄

[@SKARTHIKSELVAN]

Thanks for your efforts. If you get a chance, please make Linear algebra videos related to numerical methods.

[@drpeyam]

Coming soon

[@arrow0seb]

Love the thumbnail 😂

[@himanshivatsay6006]

love from India

[@Cow.cool.]

Wtf i was just reading this chapter in linear algebra done right 😭

[@peterbrough2461]

"I'll be Bach"

[@LarryRiedel]

Imagine if this weren't true. The whole linear algebra house of cards would collapse. :-)