Let K = R and V := R [ t ] 2 and let F : R [ t ] 2 → R [ t ] 2 , f ↦ f ( 0 ) + f ( 1 ) ⋅ ( t + t 2 )Want to calculate M S S ( F ), the transformation Matrix of F with Basis S, being the standardbasis for the polynomialring S = ( 1 , t , t 2 )So we have to use the coordinate isomorphism: M S S ( F ) = ( I S ( F ( 1 ) ) I S ( F ( t ) ) I S ( F ( t 2 ) ) ) Already know the solution, however I have no idea why the following matrix is the transformation Matrix of F. M S S ( F ) = ( 1 0 0 1 1 1 1 1 1 ) Looking at the transformation matrix we know that F ( 1 ) = 1 + t + t 2 ?

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Let   K  =  R and   V  :=  R  [  t      ]    2   and let   F  :  R  [  t      ]    2    →  R  [  t      ]    2    ,  f  ↦  f  (  0  )  +  f  (  1  )  ⋅  (  t  +      t    2    )Want to calculate       M      S      S    (  F  ), the transformation Matrix of F with Basis S, being the standardbasis for the polynomialring   S  =  (  1  ,  t  ,      t    2    )So we have to use the coordinate isomorphism:      M      S      S    (  F  )  =      (                                        I            S                    (          F          (          1          )          )                                      I            S                    (          F          (          t          )          )                                      I            S                    (          F          (                      t            2                    )          )                      )  Already know the solution, however I have no idea why the following matrix is the transformation Matrix of F.      M      S      S    (  F  )  =      (                            1                          0                          0                                      1                          1                          1                                      1                          1                          1                      )  Looking at the transformation matrix we know that   F  (  1  )  =  1  +  t  +      t    2  ?

zalitiaf · Accepted Answer

Given a polynomial   f  (  t  )  ∈  V,  F  (  f  (  t  )  )  =  f  (  0  )  +  f  (  1  )  (  t  +      t    2    )  .So, when   f  (  t  )  =  1, we have   f  (  0  )  =  f  (  1  )  =  1 and then   F  (  1  )  =  1  +  1  (  t  +      t    2    )  =  1  +  t  +      t    2

Micaela Simon · Accepted Answer

Thanks for the fast reply! I think I almost got it,   f  (  t  )  =  t we have   f  (  0  )  =  f  (  1  )  =  t? Could you tell me what happens in this case I think it will help me understand it better. I&#039;ve never seen anything like this before and to me it just seems a weird way of writing a function.

Let K = <mi mathvariant="double-struck">R and V := <mi mathvariant="double-str

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