Jump to content
  • Advertisement
Sign in to follow this  
donjonson

question checknig if a set of vectors span a vector space(REFRASED)

This topic is 4869 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

my question is this... If I have a set of n vectors in Rn, and that set is linearly dependant, is it possible for that set to span Rn? I hope that is a clearer question :) [Edited by - donjonson on July 17, 2005 3:42:11 PM]

Share this post


Link to post
Share on other sites
Advertisement
Quote:
Original post by donjonson
If I have a set of n vectors in Rn, and that set is linearly dependant, is it possible for that set to span Rn?


No, in order to span Rn, you need at least n linearly independent vectors. I think, however, you probably meant independent and not dependant. In that case, I'm not sure what the conditions are...being independent might be sufficient.

[Edited by - Promit on July 17, 2005 6:32:06 PM]

Share this post


Link to post
Share on other sites
Short answer: no.

Long answer: A linearly dependent set of n vectors can not span Rn. If you have a linearly dependent set of vectors u1, u2,... un that span a space Un then you could just remove the vectors that can be expressed as a linear combination of the others until you have a linearly independent subset u1, u2,... uk (k<n) which stills spans Un. Problem is, you need at least n vectors to span Rn, so you're screwed.

Edit: Never saw your post right above mine, I was answering your original question, sorry if you got confused.

[Edited by - GameCat on July 18, 2005 6:08:03 PM]

Share this post


Link to post
Share on other sites
Quote:
Original post by donjonson
so in other words, any set of n vectors span Rn then it is also a basis for Rn?


Yes. And furthermore, you can use Graham-Schmidt orthonormalization to come up with an orthonormal basis for Rn.

Share this post


Link to post
Share on other sites
Sign in to follow this  

  • Advertisement
×

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

We are the game development community.

Whether you are an indie, hobbyist, AAA developer, or just trying to learn, GameDev.net is the place for you to learn, share, and connect with the games industry. Learn more About Us or sign up!

Sign me up!