Recent content by pgandalf

\left\{{\begin{bmatrix}{1}&{0}\\{0}&{0}\end{bmatrix},\begin{bmatrix}{0}&{1}\\{1}&{0}\end{bmatrix},\begin{bmatrix}{0}&{0}\\{0}&{1}\end{bmatrix}}\right\} However, what I needed to know was if the dimension was 3 because 3= Dim N(T) + Dim Im(T) and Dim Im(T)< or equal to Dim W that is equal to 3...

Yes, that's it. Now I understand. Thank you both!

I mean the dimension like R3 is a vectorial space of dimension 3 and it's isomorph to the three dimensional space, R2 is has dimension 2 and is isomorph to the plane (2D), the space of polynomials of grade lower or equal to n has a dimension of n+1 and so on...but how do we know the dimension of...

How do we calculate the dimension of a matrix? Is it the number of entries? Or is it the number of different entries? For instance if I have a matrix 2x2 the dimension would be 4 but if the matrix is simetrical it would be 3. Is this correct? Thanks for your help.

You were right! I took p(t)=t+1 and p(t)=t+2 and I made the inner product of each of them with q(t)=a+b(t) and then I used T(p)=p(\alpha) (hyphotesis of the problem) and I equalled it to <p,q> (because of the formula of the representative of riesz, T(p)=<p,q> ) and I solved the system and I...

Homework Statement Find the representative of riesz of the following linear transformation: \mathbb{T:}P_1\rightarrow{R} defined by \mathbb{T}\left ( p \right )\mathbb{=}p\left ( \alpha \right ) where \alpha is a fixed real number (Considering in P_1 the inner product...