Finding the Complements of W in R^4 to Orthogonal Vectors and Systems

  • Thread starter Thread starter transgalactic
  • Start date Start date
  • Tags Tags
    Orthogonal
Click For Summary
SUMMARY

The discussion focuses on finding the orthogonal complement \( W^\perp \) of a subspace \( W \) in \( \mathbb{R}^4 \). The user successfully identified one vector in the complement as (-1, 1, 0, 0). The task involves determining additional vectors that are orthogonal to this vector, which collectively form a basis for the complement space \( W^\perp \), a subspace of \( \mathbb{R}^3 \).

PREREQUISITES
  • Understanding of vector spaces and subspaces in linear algebra
  • Knowledge of orthogonality and orthogonal complements
  • Familiarity with the properties of \( \mathbb{R}^n \) spaces
  • Basic skills in solving systems of linear equations
NEXT STEPS
  • Study the Gram-Schmidt process for orthogonalization of vectors
  • Learn how to compute the null space of a matrix to find orthogonal complements
  • Explore the concept of bases and dimension in vector spaces
  • Investigate applications of orthogonal complements in linear transformations
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, as well as educators teaching vector space concepts.

transgalactic
Messages
1,386
Reaction score
0
W is sub space of [tex]R^4[/tex] which is defined as
http://img21.imageshack.us/img21/1849/63042233.th.gif

find the system that defines the complements [tex]W^\perp[/tex] of W
i have solved the given system and i got one vector (-1,1,0,0)
so its complement must be of R^3 and each one of the complements vectors are
orthogonal to it

how to find them
??
 
Last edited by a moderator:
Physics news on Phys.org
solved it :)
 

Similar threads

Prove the W is the orthogonal complement of its orthogonal complement
  • · Replies 2 ·
Replies
2
Views
10K
Finding Orthogonal Unit Vector to 3 Vectors
  • · Replies 1 ·
Replies
1
Views
2K
Finding an orthogonal complement without an explicitly defined inner product
  • · Replies 4 ·
Replies
4
Views
3K
Orthogonal Complements of complex and continuous function subspaces
  • · Replies 3 ·
Replies
3
Views
3K
Finding the Orthogonal Complement
  • · Replies 3 ·
Replies
3
Views
2K
Orthogonality of a curvilinear coordinate system
  • · Replies 11 ·
Replies
11
Views
3K
Is a Vector Orthogonal to a Set Also Orthogonal to Its Span?
  • · Replies 8 ·
Replies
8
Views
2K
Null space of dual map of T = annihilator of range T
  • · Replies 1 ·
Replies
1
Views
3K
Solving for Orthogonal Vectors in R4?
  • · Replies 3 ·
Replies
3
Views
3K
Orthogonal complement of a subspace
  • · Replies 3 ·
Replies
3
Views
10K