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Question: Bug in Gram Schmidt command

Question:Bug in Gram Schmidt command

awass 296
October 08 2018
0

From the help pages for the Gram Schmidt command:

The number of Vectors returned is the dimension of the vector space spanned by V.  In particular, if the Vectors in V are not linearly independent, fewer Vectors than the number in V are returned.


That is not what happens when floating point numbers are involved, for example:

>restart;
>with(LinearAlgebra);
>a := Vector([1, 2, 3]); b := Vector([1, -2, 3]); c := Vector([3, 2, 1]); d := Vector([5, 1, -3]); e := Vector([0, 1.01, -3]);
>GramSchmidt([a, b, c, d, e]);

This returns 3 vectors as it should BUT
>GramSchmidt([b, c, d, e, a]) returns 5 vectors (one of which is essentially 0).  That is definitely a bug.
 
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