Gramschmidt and scalar product
05-08-2021, 06:50 PM
Post: #5
 parisse Senior Member Posts: 1,301 Joined: Dec 2013
RE: Gramschmidt and scalar product
(05-08-2021 12:31 PM)roadrunner Wrote:  gramschmidt([1,1+x],(p,q)->2*p*q)

returns:

[1/sqrt(2),±∞*(-x-1+x+1)/sqrt(2)]

am i doing something wrong? Why is there a ±∞ in there?

-road
1+x is lineary dependent of 1, because your scalar product is defined on R.

If you want to have something more interesting define a scalar product with an integral or by evaluating p and q at some points, like
gramschmidt([1,1+x],(p,q)->subst(p,x=0)*subst(q,x=0)+subst(p,x=1)*subst(q,x=1))
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 Messages In This Thread Gramschmidt and scalar product - Tonig00 - 05-08-2021, 08:59 AM RE: Gramschmidt and scalar product - parisse - 05-08-2021, 10:34 AM RE: Gramschmidt and scalar product - roadrunner - 05-08-2021, 12:31 PM RE: Gramschmidt and scalar product - parisse - 05-08-2021 06:50 PM RE: Gramschmidt and scalar product - Tonig00 - 05-08-2021, 01:40 PM RE: Gramschmidt and scalar product - roadrunner - 05-09-2021, 11:17 AM

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