Mixing
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
asked yesterday
Dada
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.
add a comment |
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
asked yesterday
Dada
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.
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
add a comment |
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
asked yesterday
Dada
346
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
asked yesterday
Dada
346
asked yesterday
Dada
346
asked yesterday
Dada
346
asked yesterday
Dada
346
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
add a comment |
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
add a comment |
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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