- #1
Hiche
- 84
- 0
Homework Statement
The question states that we should use the Gram-Schmidt to find an orthogonal basis for W where W = span {p , q} and p(x) = 1 + x ; q(x) = 1 + 2x^2
Homework Equations
...
The Attempt at a Solution
Let [itex]\{b1, b2\}[/itex] be such a basis. Using the G-S process:
[itex]b1 = p = 1 + x[/itex]
[itex]b2 = q - proj^q _b = q - \frac{<q, b1>} { \|b1\|^2} . b1[/itex]
Is this the right way? The answer I got was [itex]\{b1, b2\}[/itex] = [itex]\{1 + x, 1/2 - x/2 + 2x^2\}[/itex]
Note that p and q belong to the set of polynomials of degrees 2 or less (i.e [itex] \in P_2[/itex]) and [itex]< , >[/itex] denotes an inner product of two components.
Also, presume I need to find further basis -- [itex]b3[/itex] -- is there a generality for [itex]bn[/itex] for example?
Last edited: