What the V*****

[@drewpat9535]

The day you'll stop smiling we'll stop watching your videos! Your enthusiasm is the key! Thanks again!!!!

[@weinihao3632]

* * * * * Five stars for Dr.Peyam! Your dual spaces playlist is fantastic. Still hope you'll extend it to infinite dimensional vectorspaces one day.

[@ibrahinmenriquez3108]

Press a gigantic F to pay respect to this amazing teacher

[@blackpenredpen]

Not going to lie, I did watch the whole video for the entertainment purpose... no idea what the ***** it was....

[@drpeyam]

Hahahahaha

[@blackpenredpen]

Ok, Peyam! This is too much for me!

[@samuelevicario8413]

Your so great! Thank you for your enthusiasm and work

[@MrRyanroberson1]

and it turns out * is just a fancy version of ^-1 all along.

[@dr.leonardhofstadtersavage6413]

Awesome👍👍👍👍👍

[@colleen9493]

Yes! I was waiting for this one! I remember in an interview with you and bprp and maybe Chester I can’t remember you said in a video you would do V*****!

[@johannesh7610]

Those Functions f are just transposed Vectors: Linear Transformations "are" Matrices, so LT from n Dimensions to 1 Dimensions are just 1×n-Matrices, that is, row vectors. So the elements of V* are Scalar multiplications with a vector in V. So (V*) * are Linear Transformations, that is, Matrices, taking those row Vectors and turning them into a Scalar. Those must therefore be Column vectors once again, the elements of V. Therefore V** is V

[@yahya5308]

ayyy , cool interpretation

[@KY-wl3ss]

what an insightful comment!

[@dgrandlapinblanc]

OK. Thank you very much.

[@LarryRiedel]

I feel like I'm going to wind up learning things like automorphism groups.

[@KY-wl3ss]

As a self-learner of linear algebra, dual space part was discouraging and your video helped me. insightful comments from experts are also helpful.

[@ezras7997]

That escalated quickly

[@djsmeguk]

press F to pay respects to HUMUNGOUS F

[@Adraria8]

We can go further!

[@youssefbenhachem993]

That's really fantastic . Thanks so much

[@unflexian]

YESS I find these videos days before my linear algebra final

[@michalbotor]

so i believe, that the gist of the video is that f(x) ≡ fx ≡ (f)x, where x ∈ V and f ∈ V*, can be interpreted twofold: either as a functional f(⋅) ∈ V* := L(V, F), i.e. a linear function f(⋅): V --> F, which evaluates f on every vector in V, or as an evaluation map (⋅)x ∈ V := L(V*, F), i.e. a linear function (⋅)x: V* --> F, which evaluates every functional in V* at x. correct? ;)

[@drpeyam]

Yeah :)

[@chinesecabbagefarmer]

I dont understand maybe ninety percent of what u say but i just like u so much i eatch every video!

[@sandorszabo2470]

This is your funniest video 😊

[@drpeyam]

I had so much fun making it 😂😂😂

[@martind2520]

You keep saying things are different with infinite dimentional vector spaces. Can you give an example? Thanks.

[@drpeyam]

For example, in infinite dimensions, V* is not isomorphic to V

[@chinesecabbagefarmer]

YAY ITS YOU

[@chinesecabbagefarmer]

I LIKE U

[@drpeyam]

Thanks ☺️

[@chinesecabbagefarmer]

@@drpeyam hahaha no need to thank me. You are just naturally a likeable person. I like to say 'earth is lucky to have you'. It is especially true about you!

[@drpeyam]

Awwwwwwww ❤️❤️❤️

[@chinesecabbagefarmer]

@@drpeyam yay u repllied 💙

[@dhunt6618]

V(ascot(balmoral(baseball(beanie(bearskin(beret(bicorne(bowler(chullo(cloche(cricket(sombrero(....(x))...) is a lot of dual hats (partially listed from wikipedia)

[@moshill1374]

Voice is really annoying, am I the only one that thinks that?

[@simpleprogrammingcodes]

For me it's fine.