1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Advanced Calc problem

  1. Apr 11, 2006 #1
    I'm having issues seeing the method to go with this problem. Here it is:

    Suppose that X is a linear space of dimension n, and E = {e1,...,en}, F = {f1,...,fn} are two bases of X. Prove that there is a unique invertible n*n matrix [sij] such that if a vector x belonging to X (I don't know how to make the math symbols or subscripts so please bare with me) has components [ai] with respect to E and components [bj] with respect to F, meaning that

    x = Summation( i=1 to n) ai*ei, x = Summation( j=1 to n) bj*fj

    ai = Summation( j=1 to n) sij*bj.

    My book doesn't give examples so I'm having a hard time seeing how to do this problem. If E and F are bases, then they're independent so the components ai and bj are unique. Then sij is just the combination of ai and bj. I'm pretty cloudy and would appreciate all the help I could get. Thanks in advance.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Advanced Calc problem Date
Advanced Calc Proof Feb 9, 2012
Advanced Calc( Derivatives) Apr 11, 2011
Advanced Calc/Analysis: Delta Epsilon proof Sep 30, 2010
Advanced Calc. Continuity problem Jun 24, 2010
Advanced calc Dec 6, 2008