Recent content by sharkboy

Isn't that just the (1...1) vector (size 1 x n)

OK - I think I was missing a key info and finally figured it out. On more reading, I realized that a linear functional maps into a scalar. Thats the key I was missing. And all the other exampls made sense then. However, this problem is not Consider the linear functional f:Rn --> R defined by...

Yes.. the way to prove is below Scalar addition f(u) = <(1,2), u> = 1*u + 2*u = u + 2u = 3u f(g) = <(1,2), g> = = 3g f(u+g) = <(1,2), (u,g)> = 1*u + 1*g + 2*u + 2*g = 3u + 3g f(u) + f(g) = f(u+g) Scalar multiplication f(kx) = <(1,2), kx> = kx*1 + 2*kx = 3kx kf(x)...

Morphism - Do I just <v,v> for the linear functional. I don't clearly understand what the other term I need. Sharkie

Wasn't clear in my last post: there were 2 questions 1- So in the inner product (in planetmath.org) what is x? 2- What is definition of inner product.

So in the inner product what is x? What is definition of inner product.

How do I solve this problem- I know it has something to do Riesz represenation but am having difficulty connecting dots Conside R4 with usual inner product. Find the linear funcitonal associated to the vector (1,1,2,2). What am I missing- is this problem complete or is there something...