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

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

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Roger Stafford

Posts: 5,811
Registered: 12/7/04
Re: What am I missing?
Posted: Nov 22, 2012 6:18 PM
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"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

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