Recent content by reha

Whatever you have T acting on, the result is a scalar multiple of v, is it not? Namely, <x,v>v, where <x,v> is said scalar. Please explain again. i don't get why it is scalar? i thought x and y are vectors. This is right und means that the zero vector is in the kernel of T. (This is true for...

Thanks. Can you please tell me if the following is correct: f(x)= <x,v>v say a is scalar. and s be a vector. hence f(x)= <(ax+s), v>v = axv^2 + sv^2 Thanks. Please correct my mistake. Btw, why can't i use the symmetry property which i had used earlier?

f is a mapping. where mapping f(x)= <x,v>v Inner product properties: linearity, symmetry (which i had used) and definiteness. should i need to use all of them? Thanks.

for 1) f(x)=<x,v>v. Show f is a linear transformation. since <x,v> = <v,x> (symmetry) hence <x,v>v = <v,x>v = vT x v = x == f(x). Am i right? but i feel its absurd. (vT is v transpose) range and kernel. Range ( please help me out. I've no idea how to describe it. thanks) Kernel. i...

for 1) f(x)=<x,v>v. Show f is a linear transformation. since <x,v> = <v,x> (symmetry) hence <x,v>v = <v,x>v = vT x v = x == f(x). Am i right? but i feel its absurd. (vT is v transpose) range and kernel. Range ( please help me out. I've no idea how to describe it. thanks) Kernel. i...

If V is a vector space with an inner space <.,.>. V1 is an non empty subset of V. Vector x is contained in V is said to be orthogonal to v1 if <x,y>=0 for all y contained in V1. 1) if v is contained in V and define the mapping f(x)=<x,v>v. Show f is a linear transformation and describe its...

let pf(x)= sum( from i=1 to k) <x, ui>ui, show pf is a projection. Ive tried to show this fact myself but i failed. Please some one help me out. thanks Note ui = u1...un an orthogonal basis of V where V is a vector space.