How can i create n-linearly independent vectors?
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Like 4-linearly independent vectors if n=4 as follows
a1=[1,17] , a2=[1,7] , a3=[1,1] , a4=[1,9]
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James Tursa
le 11 Mar 2015
Modifié(e) : James Tursa
le 11 Mar 2015
The simplest thing to do I suppose is just to pick off the columns of the identity matrix of the appropriate size. Do you have any other criteria that needs to be met?
I should add that your example will not work ... you can't have four linearly independent 2-element vectors, since two linearly independent 2-element vectors will span the entire space.
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Roger Stafford
le 11 Mar 2015
You can also use matlab's 'orth' function to generate linearly independent vectors which span a given space. They will in fact be orthogonal. See:
http://www.mathworks.com/help/matlab/ref/orth.html
(Note: You cannot get four linearly independent vectors from your set of two-element vectors. The maximum would be two. For example, in the vectors you give, there is the equality:
3*a1-8*a2+5*a3 = 0
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