Register to reply 
Inner product space  minimization. 
Share this thread: 
#1
Apr513, 04:14 PM

P: 219

The question is : If the vector space C[1,1] of continuous real valued functions on the interval [1,1] is equipped with the inner product defined by (f,g)=[itex]^{1}_{1}[/itex] [itex]\intf(x)g(x)dx[/itex]
Find the linear polynomial g(t) nearest to f(t) = e^t? So I understand the solution will be given by (u1,e^t).u1 + (u2,e^t).u2 But I am having trouble understanding what u1 and u2 should be. I understand they must be othorgonal and basis for a subspace S [itex]\in[/itex] C[1,1]. However Im not too sure what dimension this basis should be of, and not 100% sure what is meant by the vector space C[1,1]. (The solution uses 1 and t as u1 and u2....) Many thanks in advance for any assistance. 


#2
Apr513, 09:47 PM

Homework
Sci Advisor
HW Helper
Thanks ∞
P: 9,643

I think you're making it overcomplicated. Isn't it just asking for the affine function g(t) which minimises the integral for the given f(t)?



Register to reply 
Related Discussions  
Vector space or inner product space  ambiguous!  Linear & Abstract Algebra  27  
Inner Product Space  Calculus & Beyond Homework  1  
Inner Product Space/Hilbert Space Problem  Calculus & Beyond Homework  1  
Product space  Differential Geometry  4  
Normed linear space and inner product space  Calculus & Beyond Homework  8 