
#1
Nov507, 01:55 PM

P: 87

Let S be a linearly independent set of vectors from the finite dimensional vector space V. Prove that there exists a basis for V containing S. Can anyone help me out? I can't figure out how to approach this.




#2
Nov507, 02:48 PM

Sci Advisor
HW Helper
P: 4,301

What is a basis? What do you need to have one? What do you already have? Can you think of a way to construct the rest?




#3
Nov507, 04:36 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,896

If the independent set already spans the space, you are done. If not then there exists a vector that cannot be written as a linear combination of the vectors in the independent set. Can you show that adding that new vector to the set still gives you an independent set of vectors? If that new set spans the vector space, you are done. If not ....



Register to reply 
Related Discussions  
matrix connecting Sz diagonal basis to Sx diag basis  Quantum Physics  0  
Basis on R^3  Calculus  1  
Basis independent and basis dependent formulation of QM  Advanced Physics Homework  0  
free basis and basis?  Calculus & Beyond Homework  7  
prove a tensor product  Differential Geometry  37 