Is there a math operator to see if all vector element values are positive?

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So I want to check if all vector values are positive and if they are get 1 else a 0. Is there an operator for that or one must use a picewize function?



So
$P[1,2,0]^t = 1$



while



$P[-1,0,0]^t = 0$




operator-theory




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  • Please give an example of when a "vector value is positive".
    – coffeemath
    Aug 13 at 3:20














up vote
0
down vote

favorite
1












So I want to check if all vector values are positive and if they are get 1 else a 0. Is there an operator for that or one must use a picewize function?



So
$P[1,2,0]^t = 1$



while



$P[-1,0,0]^t = 0$




operator-theory




share|cite|improve this question






















  • Please give an example of when a "vector value is positive".
    – coffeemath
    Aug 13 at 3:20












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





So I want to check if all vector values are positive and if they are get 1 else a 0. Is there an operator for that or one must use a picewize function?



So
$P[1,2,0]^t = 1$



while



$P[-1,0,0]^t = 0$




operator-theory




share|cite|improve this question














So I want to check if all vector values are positive and if they are get 1 else a 0. Is there an operator for that or one must use a picewize function?



So
$P[1,2,0]^t = 1$



while



$P[-1,0,0]^t = 0$





operator-theory





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 13 at 3:22

























asked Aug 13 at 3:18









DuckQueen

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1377











  • Please give an example of when a "vector value is positive".
    – coffeemath
    Aug 13 at 3:20
















  • Please give an example of when a "vector value is positive".
    – coffeemath
    Aug 13 at 3:20















Please give an example of when a "vector value is positive".
– coffeemath
Aug 13 at 3:20




Please give an example of when a "vector value is positive".
– coffeemath
Aug 13 at 3:20










2 Answers
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To test whether each component is positive is equivalent to testing if the minimum is positive.:$$Px = mathbb1_min_i x_i >0$$






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    If the vector $vec P$ has $N$ components then



    $$ T equiv sum_k=1^N big ( |P_k|-P_k big) =0 $$



    if and only if all components are non-negative.



    a function that gives the values you want can be expressed as $(T = 0)$ understood as a boolean function returning 1 for true and 0 for false






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      2 Answers
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      2 Answers
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      up vote
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      To test whether each component is positive is equivalent to testing if the minimum is positive.:$$Px = mathbb1_min_i x_i >0$$






      share|cite|improve this answer
























        up vote
        1
        down vote













        To test whether each component is positive is equivalent to testing if the minimum is positive.:$$Px = mathbb1_min_i x_i >0$$






        share|cite|improve this answer






















          up vote
          1
          down vote










          up vote
          1
          down vote









          To test whether each component is positive is equivalent to testing if the minimum is positive.:$$Px = mathbb1_min_i x_i >0$$






          share|cite|improve this answer












          To test whether each component is positive is equivalent to testing if the minimum is positive.:$$Px = mathbb1_min_i x_i >0$$







          share|cite|improve this answer












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          answered Aug 13 at 3:28









          Siong Thye Goh

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              up vote
              0
              down vote













              If the vector $vec P$ has $N$ components then



              $$ T equiv sum_k=1^N big ( |P_k|-P_k big) =0 $$



              if and only if all components are non-negative.



              a function that gives the values you want can be expressed as $(T = 0)$ understood as a boolean function returning 1 for true and 0 for false






              share|cite|improve this answer
























                up vote
                0
                down vote













                If the vector $vec P$ has $N$ components then



                $$ T equiv sum_k=1^N big ( |P_k|-P_k big) =0 $$



                if and only if all components are non-negative.



                a function that gives the values you want can be expressed as $(T = 0)$ understood as a boolean function returning 1 for true and 0 for false






                share|cite|improve this answer






















                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  If the vector $vec P$ has $N$ components then



                  $$ T equiv sum_k=1^N big ( |P_k|-P_k big) =0 $$



                  if and only if all components are non-negative.



                  a function that gives the values you want can be expressed as $(T = 0)$ understood as a boolean function returning 1 for true and 0 for false






                  share|cite|improve this answer












                  If the vector $vec P$ has $N$ components then



                  $$ T equiv sum_k=1^N big ( |P_k|-P_k big) =0 $$



                  if and only if all components are non-negative.



                  a function that gives the values you want can be expressed as $(T = 0)$ understood as a boolean function returning 1 for true and 0 for false







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Aug 13 at 3:46









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