Every basis is a dual basis

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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!

Dr Peyam

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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.)

ChefSalad

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

plaustrarius

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

High_Priest_Jonko

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

Rysdan

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

Л.С.Мото

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