induced norm of a one to one function
$begingroup$
Let $V subset C^0(mathbb{R}, mathbb{R})$ be a vector space and $ f: V to mathbb{R}^n : g mapsto (g(i))_{i=1,dotsc,n}$ a one to one function.
Then in my lesson, they are talking about the norm of $V$ induced by the function $f$.
I don't understand what it is. I know that on $mathbb{R}^n$ there is the euclidian norm, but then why $f$ defined a norm on $V$ and what is this norm ?
Thank you!
real-analysis linear-algebra vector-spaces norm
edited Nov 25 '18 at 12:50
SvanN
1,9921422
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
$endgroup$
add a comment |
$begingroup$
Let $V subset C^0(mathbb{R}, mathbb{R})$ be a vector space and $ f: V to mathbb{R}^n : g mapsto (g(i))_{i=1,dotsc,n}$ a one to one function.
Then in my lesson, they are talking about the norm of $V$ induced by the function $f$.
I don't understand what it is. I know that on $mathbb{R}^n$ there is the euclidian norm, but then why $f$ defined a norm on $V$ and what is this norm ?
Thank you!
real-analysis linear-algebra vector-spaces norm
edited Nov 25 '18 at 12:50
SvanN
1,9921422
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
$endgroup$
$begingroup$
If $f$ is nonlinear, there doesn't seem to be any natural way to approach this...
$endgroup$
– SvanN
Nov 26 '18 at 13:18
add a comment |
$begingroup$
Let $V subset C^0(mathbb{R}, mathbb{R})$ be a vector space and $ f: V to mathbb{R}^n : g mapsto (g(i))_{i=1,dotsc,n}$ a one to one function.
Then in my lesson, they are talking about the norm of $V$ induced by the function $f$.
I don't understand what it is. I know that on $mathbb{R}^n$ there is the euclidian norm, but then why $f$ defined a norm on $V$ and what is this norm ?
Thank you!
real-analysis linear-algebra vector-spaces norm
edited Nov 25 '18 at 12:50
SvanN
1,9921422
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
$endgroup$
Let $V subset C^0(mathbb{R}, mathbb{R})$ be a vector space and $ f: V to mathbb{R}^n : g mapsto (g(i))_{i=1,dotsc,n}$ a one to one function.
Then in my lesson, they are talking about the norm of $V$ induced by the function $f$.
I don't understand what it is. I know that on $mathbb{R}^n$ there is the euclidian norm, but then why $f$ defined a norm on $V$ and what is this norm ?
Thank you!
real-analysis linear-algebra vector-spaces norm
real-analysis linear-algebra vector-spaces norm
edited Nov 25 '18 at 12:50
SvanN
1,9921422
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
edited Nov 25 '18 at 12:50
SvanN
1,9921422
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
edited Nov 25 '18 at 12:50
SvanN
1,9921422
edited Nov 25 '18 at 12:50
SvanN
1,9921422
edited Nov 25 '18 at 12:50
SvanN
1,9921422
1,9921422
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
asked Nov 25 '18 at 12:44
auhasardauhasard
14414
14414
$begingroup$
If $f$ is nonlinear, there doesn't seem to be any natural way to approach this...
$endgroup$
– SvanN
Nov 26 '18 at 13:18
add a comment |
$begingroup$
If $f$ is nonlinear, there doesn't seem to be any natural way to approach this...
$endgroup$
– SvanN
Nov 26 '18 at 13:18
$begingroup$
If $f$ is nonlinear, there doesn't seem to be any natural way to approach this...
$endgroup$
– SvanN
Nov 26 '18 at 13:18
$begingroup$
If $f$ is nonlinear, there doesn't seem to be any natural way to approach this...
$endgroup$
– SvanN
Nov 26 '18 at 13:18
add a comment |
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$begingroup$
If $f$ is nonlinear, there doesn't seem to be any natural way to approach this...
$endgroup$
– SvanN
Nov 26 '18 at 13:18