Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have that

|T(p)| <= sqrt(10)*|p|

where T is a linear mapping. The question is: How small must |p' - p''| be in order that |T(p') - T(p'')| <= 1/10.

This is what I did:

T linear, so

|T(p') - T(p'')| = |T(p' - p'')|.

Applying the bound:

|T(p' - p'')| <= sqrt(10)*|p' - p''|

So pick |p' - p''| = 1 / (sqrt(10)*10).

Then

|T(p' - p'')| = |T(p') - T(p'')| <= 1/10.

Is that right?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Linear transformation / analysis help

**Physics Forums | Science Articles, Homework Help, Discussion**