How to Extend and Calculate a Basis for the Whole Space

  • Thread starter boderam
  • Start date
  • #1
24
0

Main Question or Discussion Point

For example, say you start out with (2,1,0) and (2,0,2). Well the easiest answer here is to think of these two vectors in a plane, so you should take the cross product to get the vector that is not in the plane, and there you have a basis for R^3. But how about when we run into similar problems in R^n, not just when we are given n-1 vectors, but perhaps any m less than n. What would be the systematic method?
 

Answers and Replies

  • #2
236
0
Do a change of coordinates so that the given n vectors are each zero except for a 1 in the n-th position. It should then be obvious how to extend.
 
  • #3
24
0
How do you do the change of basis so this happens? My memory is vague about this.
 

Related Threads for: How to Extend and Calculate a Basis for the Whole Space

  • Last Post
Replies
6
Views
23K
Replies
1
Views
2K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
3
Views
2K
Replies
2
Views
2K
  • Last Post
10
Replies
228
Views
27K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
1
Views
3K
Top