What is...the dual vector space?

Goal.
Explaining basic concepts of linear algebra in an intuitive way.

This time.
What is...the dual vector space? Or: Two flipped sides.

Slides.

Nonsense.
It should be “ac + bd” and not “ac + bc” on the “The transpose space” slide.
On the final slide the second vector was suppose to be (1/2,1/2,1/2).

Nonsense.
There is a typo on one of the slides, see the comments below.

#linearalgebra
#algebra
#mathematics

[Manoosbi]

This video is a blessing! I was googling about dual spaces for hours hoping to find so kind of illustrated explanation about the topic and I can say hands down that this video is the best explanation I found on dual spaces! It"s impressive how you managed to make it so clear and intuitive! I'm so glad I found your video. Many thanks!

[sudhagarraghavan]

Outstanding explanation on the concept of dual vector space, thank you! Most videos focused on the mathematical nuts and bolts of the topic but not the reason "why" and the big picture.

[sumbunny]

I don't know if you will see this but so what is the exact difference between the transpose vector space and the dual space? Are they basically the same thing or is there a difference between them? I can't really find anything on it. Like what is the relationship between both of these things

[sudhagarraghavan]

BTW I noticed a typo in your slide titled "Transpose Space". The product of row vector and column vector should be ac + bd and not ac + bc.

[Soyutkita]

thank you so much! I'm glad I've found your chanel

[AkamiChannel]

Yup, other sources on youtube that explain this topic are basically garbage compared to yours. My channel is with a graphics-programming bias, but I hope to carry the torch and pass down lucid explanations like yours in the future! Thank you! And you gained a subscriber today.

[pavel]

This is a jaw dropping explanation ! Thank you so much! Just one question: What is the capital K at the 14.55 mark as part of the Definition of V* ?

[er]

15:37 it should be f*(\phi) = \phi compose f . The star is missing

[AkamiChannel]

Btw is there some software you used to make the diagrams at the end? Or were they downloaded from the internet?

[sakcee]

Dr. Tubbenhauer, Thanks for the great videos! what linear algebra books are your favorites? if you have to recommend 3 books to a beginner, which ones you would suggest?

[silversky]

I was really struggling to grasp this concept. Thank you for your video sir. It genuinely helped me.😊😊

[shafey]

Do you have any more videos that touch on duality?

[thevegg]

Would it not be a lot simpler to draw a vector and then draw it’s dual partner.
I have been searching for months to find any relation to what everybody talks about as dual basis, and that of geometry where you project a vector perpendicularly to get the dual basis