Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Software » comp.soft-sys.matlab

Topic: What am I missing?
Replies: 5   Last Post: Nov 23, 2012 5:30 PM

Advanced Search
Reply to this Topic Reply to this Topic

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Roger Stafford

Posts: 5,902
Registered: 12/7/04
Re: What am I missing?
Posted: Nov 22, 2012 6:18 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"Greg Heath" <heath@alumni.brown.edu> wrote in message <k8m4qf$8de$1@newscl01ah.mathworks.com>...
> >>A1= round(rand(1,5))
> A2 = 1-A1
> A = [ A1 ; A2 ]
> Why isn't rankA = 1?
- - - - - - - - -
For A1 and A2 to be linearly dependent requires that there exist two real or complex numbers, c1 and c2, not both zero, such that c1*A1 + c2*A2 = 0. The equality A2 = 1-A1 doesn't qualify for that. In fact A1 and A2 are linearly independent since no such c1 and c2 exist. Hence the rank of A must be 2.

Another way to see this is that the rank is the size of the largest square submatrix within A whose determinant is nonzero. Clearly this is 2.

Roger Stafford

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2015. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.