Register to reply

Linear Transformations and Isomorphisms

Share this thread:
blondie1234
#1
Apr19-10, 06:17 PM
P: 2
1. Find out which of the transformations are linear. For those that are linear, determine whether they are isomorphisms. T(f(t)) = f'(t) + t^2 from P2 to P2



2. To be linear, T(f(t)+g(t))=T(f(t)) + T(g(t)), kT(f(t))=T(f(kt))



3. After testing for linearity, I am thinking that the equation does not fulfill the requirements and therefore there are no isomorphisms, but I'm not sure if I did it right. First, I said that:
T(f(t)+g(t))=(f'(t)+g'(t))+ t^2
and T(f(t) + T(g(t))= f'(t)+t^2+g'(t)+t^2=f'(t)+2(t^2)+g'(t)
which is not equal to the first, therefore it is not linear. Am I going in the right direction with this?

1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
Phys.Org News Partner Science news on Phys.org
Climate change increases risk of crop slowdown in next 20 years
Researcher part of team studying ways to better predict intensity of hurricanes
New molecule puts scientists a step closer to understanding hydrogen storage
Dick
#2
Apr19-10, 07:10 PM
Sci Advisor
HW Helper
Thanks
P: 25,251
You are doing it right. It's not linear.


Register to reply

Related Discussions
Another linear algebra problem, basis and linear transformations. Calculus & Beyond Homework 7
Linear Algebra - Linear Transformations, Change of Basis Calculus & Beyond Homework 3
Linear Algebra (Vector spaces, linear independent subsets, transformations) Calculus & Beyond Homework 12
Linear Algebra: Linear Transformations Calculus & Beyond Homework 2