Linear maps: family and homomorphsimus [on hold]











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I have some issues with this problem, how can I show this?




Show that the family with elements $(ev_alpha)_{alpha∈mathbb{R}}$ of $mathbb{R}$-vector space $Hom_mathbb{R}(mathbb{R}[T],mathbb{R})$ is linearly independent, but not a generating set. $ev_alpha$ for $alpha ∈ mathbb{R}$ is the evaluation described by $alpha$ of polynomials, that means, the linear map $mathbb{R}[T] rightarrow mathbb{R}, f rightarrow f(alpha)$.







linear-algebra linear-transformations







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put on hold as off-topic by Omnomnomnom, jgon, user10354138, Cesareo, Shailesh yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Omnomnomnom, jgon, user10354138, Cesareo, Shailesh

If this question can be reworded to fit the rules in the help center, please edit the question.









  • 3




    Coould you specify what those 'issues' are?
    – ajotatxe
    yesterday












  • What is $T$ in this context?
    – Omnomnomnom
    yesterday










  • @Omnomnomnom It means the polinomyals, call it X if you prefer
    – Dada
    yesterday










  • Just an idea but have you tried expressing the derivative-at-some-point map as a linear combination of evaluations?
    – user25959
    yesterday















up vote
0
down vote

favorite












I have some issues with this problem, how can I show this?




Show that the family with elements $(ev_alpha)_{alpha∈mathbb{R}}$ of $mathbb{R}$-vector space $Hom_mathbb{R}(mathbb{R}[T],mathbb{R})$ is linearly independent, but not a generating set. $ev_alpha$ for $alpha ∈ mathbb{R}$ is the evaluation described by $alpha$ of polynomials, that means, the linear map $mathbb{R}[T] rightarrow mathbb{R}, f rightarrow f(alpha)$.







linear-algebra linear-transformations







share|cite|improve this question













put on hold as off-topic by Omnomnomnom, jgon, user10354138, Cesareo, Shailesh yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Omnomnomnom, jgon, user10354138, Cesareo, Shailesh

If this question can be reworded to fit the rules in the help center, please edit the question.









  • 3




    Coould you specify what those 'issues' are?
    – ajotatxe
    yesterday












  • What is $T$ in this context?
    – Omnomnomnom
    yesterday










  • @Omnomnomnom It means the polinomyals, call it X if you prefer
    – Dada
    yesterday










  • Just an idea but have you tried expressing the derivative-at-some-point map as a linear combination of evaluations?
    – user25959
    yesterday













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have some issues with this problem, how can I show this?




Show that the family with elements $(ev_alpha)_{alpha∈mathbb{R}}$ of $mathbb{R}$-vector space $Hom_mathbb{R}(mathbb{R}[T],mathbb{R})$ is linearly independent, but not a generating set. $ev_alpha$ for $alpha ∈ mathbb{R}$ is the evaluation described by $alpha$ of polynomials, that means, the linear map $mathbb{R}[T] rightarrow mathbb{R}, f rightarrow f(alpha)$.







linear-algebra linear-transformations







share|cite|improve this question













I have some issues with this problem, how can I show this?




Show that the family with elements $(ev_alpha)_{alpha∈mathbb{R}}$ of $mathbb{R}$-vector space $Hom_mathbb{R}(mathbb{R}[T],mathbb{R})$ is linearly independent, but not a generating set. $ev_alpha$ for $alpha ∈ mathbb{R}$ is the evaluation described by $alpha$ of polynomials, that means, the linear map $mathbb{R}[T] rightarrow mathbb{R}, f rightarrow f(alpha)$.







linear-algebra linear-transformations




linear-algebra linear-transformations






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked yesterday









Dada

346




346




put on hold as off-topic by Omnomnomnom, jgon, user10354138, Cesareo, Shailesh yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Omnomnomnom, jgon, user10354138, Cesareo, Shailesh

If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Omnomnomnom, jgon, user10354138, Cesareo, Shailesh yesterday


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Omnomnomnom, jgon, user10354138, Cesareo, Shailesh

If this question can be reworded to fit the rules in the help center, please edit the question.








  • 3




    Coould you specify what those 'issues' are?
    – ajotatxe
    yesterday












  • What is $T$ in this context?
    – Omnomnomnom
    yesterday










  • @Omnomnomnom It means the polinomyals, call it X if you prefer
    – Dada
    yesterday










  • Just an idea but have you tried expressing the derivative-at-some-point map as a linear combination of evaluations?
    – user25959
    yesterday














  • 3




    Coould you specify what those 'issues' are?
    – ajotatxe
    yesterday












  • What is $T$ in this context?
    – Omnomnomnom
    yesterday










  • @Omnomnomnom It means the polinomyals, call it X if you prefer
    – Dada
    yesterday










  • Just an idea but have you tried expressing the derivative-at-some-point map as a linear combination of evaluations?
    – user25959
    yesterday








3




3




Coould you specify what those 'issues' are?
– ajotatxe
yesterday






Coould you specify what those 'issues' are?
– ajotatxe
yesterday














What is $T$ in this context?
– Omnomnomnom
yesterday




What is $T$ in this context?
– Omnomnomnom
yesterday












@Omnomnomnom It means the polinomyals, call it X if you prefer
– Dada
yesterday




@Omnomnomnom It means the polinomyals, call it X if you prefer
– Dada
yesterday












Just an idea but have you tried expressing the derivative-at-some-point map as a linear combination of evaluations?
– user25959
yesterday




Just an idea but have you tried expressing the derivative-at-some-point map as a linear combination of evaluations?
– user25959
yesterday















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