Every basis is a dual basis

In this video, I show a very neat result about dual spaces: Namely, any basis of V* is automatically a dual basis of some basis of V. Even though this result is very interesting, it's the proof that makes this very exciting, by simply using the fact that V and V** are 'very' isomorphic. Enjoy!
Example: • Reverse Dual Basis
V and V** are isomorphic: • Double Dual
Check out my dual spaces playlist: • Reverse Dual Basis
Subscribe to my channel: / drpeyam

[@plaustrarius]

Every basis is a dual basis!! Amazing thumbnail, I audibly laughed

[@ChefSalad]

I have decreed the following:
Functions are black-boxes which take in numbers and spit out numbers.
Functionals take in functions and spit out numbers.
Functionalities take in functionals and spit out numbers.
Functionalitations take in functionalities and spit out numbers.
Functionalitationals take in functionalitations and spit out numbers.
Functionalitationalities takes in functionalitationals and spit out numbers. And so on to infinity.
(For the purpose of the discussion, vectors are just another type of number.)

[@theproofessayist8441]

hahahahhaahahaha!

[@abbeleon]

Not to be seditious, but how about the sequence: function, functional, functionalal, functionalalal,..., function(k)al,... where k denotes the number of stars on V?
This allows for justified public use of the otherwise annoying "-alalalalalal." Cosider also the value of a rendition of Rihannas umbrella that goes like: 🎶under my function-alal, alal, alal 🎶

[@ChefSalad]

@@abbeleon your proposal makes sense and is what a sane mathematician use. Mine was more of a joke than anything real. We'll use yours when we're serious and mine when we're not. Ha-5-ha lol

[@High_Priest_Jonko]

I admire your professionalism, it distinguishes you from that obnoxious "FlammableMaths" meme channel. Keep up the great work!

[@franciscoabusleme9085]

Sydney Carton he has great content though

[@High_Priest_Jonko]

@@franciscoabusleme9085 I agree, shame that it's unwatchable. I appreciate that he's having fun with math, but I can't stomach it.

[@drpeyam]

Sydney Carton Thank you very much ☺️☺️☺️

[@dgrandlapinblanc]

OK. Thank you very much.

[@khanster]

"All about that bass-is"

[@Rysdan9]

@Dr Peyam could you please do videos on Green's Functions? Thank you.

[@user-sj2vg8hb5q]

I thought for a moment that's you on the thumbnail

[@drpeyam]

Hahahaha