I had a few questions continuing off from the slide at 2:30. 1. Must u and v exist in a particular dimension of coordinate space (e.g. R^2 or R^3) for their span to create a plane? 2. Is it only a sum of two vectors that creates a plane? Could I get shapes other than a plane by adding more than two vectors in the R^3 and above real coordinate spaces. 3. Last, does a vector that exist in R^2 also exist in R^3.
1. If you're working in higher-dimensional space (R^4 and up), then the span of two independent vectors is a higher-dimensional analogue of a plane. 2. The *span* of two independent vectors is a plane; the *sum* of two vectors is just another vector. If you span more than two vectors, you can get higher-dimensional spaces (but those don't have convenient names). 3. You can think of a vector in R^2 (say, (4, -7)) as being "embedded" in higher dimensions by tacking on zeroes at the end. So a copy of the vector (4, -7) exists in R^3 as (4, -7, 0).
@@HamblinMath Thanks for the help. I hope you don't mind me asking if my understanding of question 3 is correct: The information contained by a vector in R^2 can be expressed by a vector in R^3 by adding a '0 entry' to the R^2 vector. For example, I can represent the vector (4, -7) as (4, -7, 0). However, as a mathematical convention, the vector (4, -7) is only defined in R^2.
It’s 4am and I’ve been trying to understand this from my textbook for a while. 9 minutes on here was all I needed- cheers buddy!
I was so confused about what "span" actually meant. Thank you for this video!
Beautiful explanation of Span
Indeed
this man is carrying my module on his back and he is doing better than my lecturer
3 year and 5 months later, you are still saving lives!!
Best explaination so ever to clear our concept love and support from ANANTNAG Kashmir J&K Indians occupied kashmir J&K
Only Kashmiri's living in Indian occupied Kashmir do study. People living in POK are savages. I just hope that your future is bright my brother 💖💖
Great explanation.
Sir it is only y u who cleared our confusion but Indians don't know
damn you make it all seem so easy, kudos !
Really appreciate your help.
Thank you
thanks sir, from turkey :)
Tbh Northwestern's undergraduate teaching sucks. Thank you so much for your videos!
excellent explain sir. tahnks
Excelent!
pure Gold
In short, Thanku.
I had a few questions continuing off from the slide at 2:30.
1. Must u and v exist in a particular dimension of coordinate space
(e.g. R^2 or R^3) for their span to create a plane?
2. Is it only a sum of two vectors that creates a plane? Could I get
shapes other than a plane by adding more than two vectors in the
R^3 and above real coordinate spaces.
3. Last, does a vector that exist in R^2 also exist in R^3.
1. If you're working in higher-dimensional space (R^4 and up), then the span of two independent vectors is a higher-dimensional analogue of a plane.
2. The *span* of two independent vectors is a plane; the *sum* of two vectors is just another vector. If you span more than two vectors, you can get higher-dimensional spaces (but those don't have convenient names).
3. You can think of a vector in R^2 (say, (4, -7)) as being "embedded" in higher dimensions by tacking on zeroes at the end. So a copy of the vector (4, -7) exists in R^3 as (4, -7, 0).
@@HamblinMath
Thanks for the help. I hope you don't mind me asking if my understanding of question 3 is correct:
The information contained by a vector in R^2 can be expressed by a vector in R^3 by adding a '0 entry' to the R^2 vector. For example, I can represent the vector (4, -7) as (4, -7, 0). However, as a mathematical convention, the vector (4, -7) is only defined in R^2.
@@gaussianelimination197 Yes, (4, -7) and (4, -7, 0) are different, but closely related.
I'm still with you