What is a Vector Space?

This video explains what a vector space is an looks at R^n. Hopefully this will help you understand linear algebra. The idea of vector spaces is key to linear algebra.

Just to review the basic idea of a vector space is, a space in which you can:

- Add any two vectors together
- Or multiply by any scalar

... and still be within that that space.

[AlanMedina]

This video is really helping me understand vector space, yay.

[samhafkenscheid]

Thank you for making these videos, it has been very helpful.

[gangaprasadtewary]

could you please explain the relationship between no of coordinates and dimension of a vector space?
Also, explain the meaning of a vector except the definition that a vector is an element of a vector space

[domojim]

I'm still confused.... What exactly do you mean by a space? Is it like a domain and range that the vectors fall under?
Can't the yz-plane or xz-plane also be the R^2 vector space? How do we distinguish?

[lebongjames]

This video is Incorrect. The plane z=1 is not a vector space but follows the rules you provided. More specifically, vector spaces need to contain additive identities, multiplicative identities, and tend to contains the zero vector in some way shape or form (0, 0 vector, zero polynomial, zero function...and so on and so forth.)

[xXBRDNXx]

Increase video speed to decrease accent lol