# Question in the analysis

• Dec 4th 2012, 01:15 AM
soso123
Question in the analysis
• Dec 4th 2012, 03:04 AM
emakarov
Re: Question in the analysis
This is pretty easy. For i), there is no function S, whether linear or not, such that ST = id.
• Dec 4th 2012, 04:58 AM
HallsofIvy
Re: Question in the analysis
Notice that once you have taken $\displaystyle T(\lambda_1, \lambda_2, \lambda_3, \cdot\cdot\cdot)= (\lambda_2, \lambda_3, \lambda_4, \cdot\cdot\cdot)$ you have lost all information on $\displaystyle \lambda_1$. There is no way to know what $\displaystyle \lambda_1$ is in order to regain it. A more technical way of saying that is that T is not "one to one". Many different vectors $\displaystyle (\lambda_1, \lambda_2, \lambda_3, \cdot\cdot\cdot)$ will be mapped into the same $\displaystyle (\lambda_2, \lambda_3, \lambda_4, \cdot\cdot\cdot)$.

As for the second problem, the only difficulty is that there are an infinite number of correct answer- just choose one.
• Dec 4th 2012, 07:35 AM
soso123
Re: Question in the analysis
Thank you very much