When is a function positively homogeneous?
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-2
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For example, if my function is:
f(x) = 3
How do I establish if it's positively homogeneous or not?
functional-analysis
asked Nov 14 at 18:25
Sofia
11
add a comment |
up vote
-2
down vote
favorite
For example, if my function is:
f(x) = 3
How do I establish if it's positively homogeneous or not?
functional-analysis
asked Nov 14 at 18:25
Sofia
11
Show that $f(alpha x)=alpha^kf(x) $ for some $alpha>0$ and $kinmathbb{R}$
– Yadati Kiran
Nov 14 at 18:29
how do i do it with the example above?
– Sofia
Nov 14 at 20:24
Actually I stated it wrong. We show that $f(alpha x)=alpha^kf(x)$ for all $alpha>0$ and for some $kinmathbb{R}$. So if $alpha=1$ then its trivial. If not then take $k=0$. The function is positively homogenous.
– Yadati Kiran
Nov 15 at 7:17
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
For example, if my function is:
f(x) = 3
How do I establish if it's positively homogeneous or not?
functional-analysis
asked Nov 14 at 18:25
Sofia
11
For example, if my function is:
f(x) = 3
How do I establish if it's positively homogeneous or not?
functional-analysis
functional-analysis
asked Nov 14 at 18:25
Sofia
11
asked Nov 14 at 18:25
Sofia
11
asked Nov 14 at 18:25
Sofia
11
asked Nov 14 at 18:25
Sofia
11
asked Nov 14 at 18:25
Sofia
11
11
Show that $f(alpha x)=alpha^kf(x) $ for some $alpha>0$ and $kinmathbb{R}$
– Yadati Kiran
Nov 14 at 18:29
how do i do it with the example above?
– Sofia
Nov 14 at 20:24
Actually I stated it wrong. We show that $f(alpha x)=alpha^kf(x)$ for all $alpha>0$ and for some $kinmathbb{R}$. So if $alpha=1$ then its trivial. If not then take $k=0$. The function is positively homogenous.
– Yadati Kiran
Nov 15 at 7:17
add a comment |
Show that $f(alpha x)=alpha^kf(x) $ for some $alpha>0$ and $kinmathbb{R}$
– Yadati Kiran
Nov 14 at 18:29
how do i do it with the example above?
– Sofia
Nov 14 at 20:24
Actually I stated it wrong. We show that $f(alpha x)=alpha^kf(x)$ for all $alpha>0$ and for some $kinmathbb{R}$. So if $alpha=1$ then its trivial. If not then take $k=0$. The function is positively homogenous.
– Yadati Kiran
Nov 15 at 7:17
Show that $f(alpha x)=alpha^kf(x) $ for some $alpha>0$ and $kinmathbb{R}$
– Yadati Kiran
Nov 14 at 18:29
Show that $f(alpha x)=alpha^kf(x) $ for some $alpha>0$ and $kinmathbb{R}$
– Yadati Kiran
Nov 14 at 18:29
how do i do it with the example above?
– Sofia
Nov 14 at 20:24
how do i do it with the example above?
– Sofia
Nov 14 at 20:24
Actually I stated it wrong. We show that $f(alpha x)=alpha^kf(x)$ for all $alpha>0$ and for some $kinmathbb{R}$. So if $alpha=1$ then its trivial. If not then take $k=0$. The function is positively homogenous.
– Yadati Kiran
Nov 15 at 7:17
Actually I stated it wrong. We show that $f(alpha x)=alpha^kf(x)$ for all $alpha>0$ and for some $kinmathbb{R}$. So if $alpha=1$ then its trivial. If not then take $k=0$. The function is positively homogenous.
– Yadati Kiran
Nov 15 at 7:17
add a comment |
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Show that $f(alpha x)=alpha^kf(x) $ for some $alpha>0$ and $kinmathbb{R}$
– Yadati Kiran
Nov 14 at 18:29
how do i do it with the example above?
– Sofia
Nov 14 at 20:24
Actually I stated it wrong. We show that $f(alpha x)=alpha^kf(x)$ for all $alpha>0$ and for some $kinmathbb{R}$. So if $alpha=1$ then its trivial. If not then take $k=0$. The function is positively homogenous.
– Yadati Kiran
Nov 15 at 7:17