How best to denote an elementwise function of a vector?
$begingroup$
Consider a vector $pmb{v}=(v_1, v_2...,v_n) in mathbb{R}^n$ and a function $f: mathbb{R} to mathbb{R} $. What is the best way to denote the vector $(f(v_1), f(v_2)....,f(v_n))$?
Writing $f(pmb{v})$ isn't exactly correct as $f$ is not $mathbb{R}^n to mathbb{R}^n$.
Edit: Based on comment below - imagine dimension of $pmb{v}$ here is not known ahead of time.
notation
edited Jan 7 at 19:31
EdOverflow
25519
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
$endgroup$
add a comment |
$begingroup$
Consider a vector $pmb{v}=(v_1, v_2...,v_n) in mathbb{R}^n$ and a function $f: mathbb{R} to mathbb{R} $. What is the best way to denote the vector $(f(v_1), f(v_2)....,f(v_n))$?
Writing $f(pmb{v})$ isn't exactly correct as $f$ is not $mathbb{R}^n to mathbb{R}^n$.
Edit: Based on comment below - imagine dimension of $pmb{v}$ here is not known ahead of time.
notation
edited Jan 7 at 19:31
EdOverflow
25519
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
$endgroup$
1
$begingroup$
You could define $g:Bbb R^ntoBbb R^n text{via} g((v_1,v_2,...,v_n))=(f(v_1),f(v_2),...,f(v_n))$ and write $g(mathbf v)$ for future usage?
$endgroup$
– Shubham Johri
Jan 7 at 18:57
$begingroup$
Issue is that the length of vector $pmb{v}$ is not known ahead of time. I can certainly get around writing the longform vector repeatedly by just redefining things, but would be good to know a proper way of denoting this stuff. It is not uncommon.
$endgroup$
– ste_kwr
Jan 7 at 19:16
$begingroup$
Is that an issue? Just change the domain and codomain of $g$ to the set of tuples.
$endgroup$
– Shubham Johri
Jan 7 at 19:23
$begingroup$
Agreed, no. But was hoping to see if there was a simpler, somewhat standardized way to do this.
$endgroup$
– ste_kwr
Jan 8 at 19:00
add a comment |
$begingroup$
Consider a vector $pmb{v}=(v_1, v_2...,v_n) in mathbb{R}^n$ and a function $f: mathbb{R} to mathbb{R} $. What is the best way to denote the vector $(f(v_1), f(v_2)....,f(v_n))$?
Writing $f(pmb{v})$ isn't exactly correct as $f$ is not $mathbb{R}^n to mathbb{R}^n$.
Edit: Based on comment below - imagine dimension of $pmb{v}$ here is not known ahead of time.
notation
edited Jan 7 at 19:31
EdOverflow
25519
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
$endgroup$
Consider a vector $pmb{v}=(v_1, v_2...,v_n) in mathbb{R}^n$ and a function $f: mathbb{R} to mathbb{R} $. What is the best way to denote the vector $(f(v_1), f(v_2)....,f(v_n))$?
Writing $f(pmb{v})$ isn't exactly correct as $f$ is not $mathbb{R}^n to mathbb{R}^n$.
Edit: Based on comment below - imagine dimension of $pmb{v}$ here is not known ahead of time.
notation
notation
edited Jan 7 at 19:31
EdOverflow
25519
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
edited Jan 7 at 19:31
EdOverflow
25519
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
edited Jan 7 at 19:31
EdOverflow
25519
edited Jan 7 at 19:31
EdOverflow
25519
edited Jan 7 at 19:31
EdOverflow
25519
25519
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
asked Jan 7 at 18:45
ste_kwrste_kwr
151111
151111
1
$begingroup$
You could define $g:Bbb R^ntoBbb R^n text{via} g((v_1,v_2,...,v_n))=(f(v_1),f(v_2),...,f(v_n))$ and write $g(mathbf v)$ for future usage?
$endgroup$
– Shubham Johri
Jan 7 at 18:57
$begingroup$
Issue is that the length of vector $pmb{v}$ is not known ahead of time. I can certainly get around writing the longform vector repeatedly by just redefining things, but would be good to know a proper way of denoting this stuff. It is not uncommon.
$endgroup$
– ste_kwr
Jan 7 at 19:16
$begingroup$
Is that an issue? Just change the domain and codomain of $g$ to the set of tuples.
$endgroup$
– Shubham Johri
Jan 7 at 19:23
$begingroup$
Agreed, no. But was hoping to see if there was a simpler, somewhat standardized way to do this.
$endgroup$
– ste_kwr
Jan 8 at 19:00
add a comment |
1
$begingroup$
You could define $g:Bbb R^ntoBbb R^n text{via} g((v_1,v_2,...,v_n))=(f(v_1),f(v_2),...,f(v_n))$ and write $g(mathbf v)$ for future usage?
$endgroup$
– Shubham Johri
Jan 7 at 18:57
$begingroup$
Issue is that the length of vector $pmb{v}$ is not known ahead of time. I can certainly get around writing the longform vector repeatedly by just redefining things, but would be good to know a proper way of denoting this stuff. It is not uncommon.
$endgroup$
– ste_kwr
Jan 7 at 19:16
$begingroup$
Is that an issue? Just change the domain and codomain of $g$ to the set of tuples.
$endgroup$
– Shubham Johri
Jan 7 at 19:23
$begingroup$
Agreed, no. But was hoping to see if there was a simpler, somewhat standardized way to do this.
$endgroup$
– ste_kwr
Jan 8 at 19:00
1
1
$begingroup$
You could define $g:Bbb R^ntoBbb R^n text{via} g((v_1,v_2,...,v_n))=(f(v_1),f(v_2),...,f(v_n))$ and write $g(mathbf v)$ for future usage?
$endgroup$
– Shubham Johri
Jan 7 at 18:57
$begingroup$
You could define $g:Bbb R^ntoBbb R^n text{via} g((v_1,v_2,...,v_n))=(f(v_1),f(v_2),...,f(v_n))$ and write $g(mathbf v)$ for future usage?
$endgroup$
– Shubham Johri
Jan 7 at 18:57
$begingroup$
Issue is that the length of vector $pmb{v}$ is not known ahead of time. I can certainly get around writing the longform vector repeatedly by just redefining things, but would be good to know a proper way of denoting this stuff. It is not uncommon.
$endgroup$
– ste_kwr
Jan 7 at 19:16
$begingroup$
Issue is that the length of vector $pmb{v}$ is not known ahead of time. I can certainly get around writing the longform vector repeatedly by just redefining things, but would be good to know a proper way of denoting this stuff. It is not uncommon.
$endgroup$
– ste_kwr
Jan 7 at 19:16
$begingroup$
Is that an issue? Just change the domain and codomain of $g$ to the set of tuples.
$endgroup$
– Shubham Johri
Jan 7 at 19:23
$begingroup$
Is that an issue? Just change the domain and codomain of $g$ to the set of tuples.
$endgroup$
– Shubham Johri
Jan 7 at 19:23
$begingroup$
Agreed, no. But was hoping to see if there was a simpler, somewhat standardized way to do this.
$endgroup$
– ste_kwr
Jan 8 at 19:00
$begingroup$
Agreed, no. But was hoping to see if there was a simpler, somewhat standardized way to do this.
$endgroup$
– ste_kwr
Jan 8 at 19:00
add a comment |
1 Answer
1
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oldest
votes
$begingroup$
You can handle this many ways. There is no consistent notation for this. Books and many programming lanuages handle it differently.
You pointed with $f(v)$ already a nice way out. It is just important to be clear on the notation, that means if it is not 100% obvious in the context define it that way.
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
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add a comment |
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1 Answer
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active
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active
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$begingroup$
You can handle this many ways. There is no consistent notation for this. Books and many programming lanuages handle it differently.
You pointed with $f(v)$ already a nice way out. It is just important to be clear on the notation, that means if it is not 100% obvious in the context define it that way.
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
$endgroup$
add a comment |
$begingroup$
You can handle this many ways. There is no consistent notation for this. Books and many programming lanuages handle it differently.
You pointed with $f(v)$ already a nice way out. It is just important to be clear on the notation, that means if it is not 100% obvious in the context define it that way.
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
$endgroup$
add a comment |
$begingroup$
You can handle this many ways. There is no consistent notation for this. Books and many programming lanuages handle it differently.
You pointed with $f(v)$ already a nice way out. It is just important to be clear on the notation, that means if it is not 100% obvious in the context define it that way.
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
$endgroup$
You can handle this many ways. There is no consistent notation for this. Books and many programming lanuages handle it differently.
You pointed with $f(v)$ already a nice way out. It is just important to be clear on the notation, that means if it is not 100% obvious in the context define it that way.
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
answered Jan 7 at 19:34
TimmathstfTimmathstf
307
307
add a comment |
add a comment |
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$begingroup$
You could define $g:Bbb R^ntoBbb R^n text{via} g((v_1,v_2,...,v_n))=(f(v_1),f(v_2),...,f(v_n))$ and write $g(mathbf v)$ for future usage?
$endgroup$
– Shubham Johri
Jan 7 at 18:57
$begingroup$
Issue is that the length of vector $pmb{v}$ is not known ahead of time. I can certainly get around writing the longform vector repeatedly by just redefining things, but would be good to know a proper way of denoting this stuff. It is not uncommon.
$endgroup$
– ste_kwr
Jan 7 at 19:16
$begingroup$
Is that an issue? Just change the domain and codomain of $g$ to the set of tuples.
$endgroup$
– Shubham Johri
Jan 7 at 19:23
$begingroup$
Agreed, no. But was hoping to see if there was a simpler, somewhat standardized way to do this.
$endgroup$
– ste_kwr
Jan 8 at 19:00