Re: orthogonal compliment

[jennifer <scrilla_12_1999@xxxxxxxxx>]
How do i find an orthonormal basis of P_2(R) s.t. the differentiation
operator(the operator that takes p to p') on P_2(R) has an upper
triangular matrix with respect to this basis.

The inner product was defined like this: <f(x),g(x)>= integral from 0
to 1 f(x)g(x) dx
[...]

All right. Do you know any basis for P_2(R) (need not be
orthonormal)? Can you write the matrix corresponding to the
differentiation operator with respect to this basis? (I am
assuming that by P_2(R) you mean the space of polynomials up
to degree 2.)

What do you know about Gram-Schmidt orthogonalization?

--
Pouya D. Tafti
p dot d dot tafti at ieee dot org
.

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