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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?

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# Linear transformation / analysis help

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